Adjoint Model Research Articles

Thermoacoustic stabilization of combustors with gradient-augmented Bayesian optimization and adjoint models

Bayesian optimization (BO) is a global optimization algorithm well-suited for multimodal functions that are costly to evaluate, e.g. quantities derived from computationally expensive simulations. Recent advances have made it possible to scale BO to high-dimensional functions and accelerate its convergence by incorporating derivative information. These developments have laid the groundwork for a productive interplay between BO and adjoint solvers, a tool to cheaply obtain gradients of objective functions w.r.t. tunable parameters in a simulated physical system. In thermoacoustics, adjoint-based optimization has previously been applied to Helmholtz solvers and low-order network models to find optimally stable combustor configurations. These studies have used conjugate gradient or quasi-Newton optimizers which can get stuck in local optima and may require many evaluations of the underlying model to find a good optimum. In this paper, we propose using gradient-augmented BO to optimize adjoint models. We consider two test cases from the thermoacoustics literature: optimizing design parameters in a 1D adjoint Helmholtz model of a Rijke tube and geometry optimization in a low-order network model of a longitudinal combustor. We show that compared to BFGS, a standard quasi-Newton method, our gradient-enhanced BO arrives at multiple, more optimal configurations using considerably fewer evaluations of the solver. This approach holds great promise for efficient thermoacoustic stabilization when designing using expensive 3D adjoint Helmholtz solvers.

Shape optimization of pipeline components

AbstractWhen it comes to shape optimization of processes and equipment in an industrial environment, adjoint methods together with computational fluid dynamics have been a great solution. The success of these methods is due to the total cost of obtaining the sensitivity derivatives once it is independent of the number of shape parameters. However, few developments for multiphase flows have been proposed, as there are still fundamental limitations in adjoint models that might prevent their common use. The adjoint theory is not applicable, for example, to the Lagrangian formulation, which has been the workhorse in particle‐induced erosion simulations. Despite these circumstances, it is intuitively possible to think that the optimization of the carrier flow is also expected to ‘optimize’ the particle flow. For instance, reducing total losses in a pipe junction will lead to a more streamlined design. This, in turn, will prevent sudden changes in fluid motion and, consequently, in particle path. As a direct outcome, erosion is expected to be mitigated, as it is mostly influenced by the particle velocity. Given the lack of rigorous mathematical proof of that, the present work investigates how the optimization of single‐phase flow can also mitigate erosion. The erosive wear problem was tackled in three different bend pipes, and the correlation with Stokes number was further explored. As general results, substantial reductions in peak erosion have been found as a consequence of minimizing total losses for all addressed cases. Accordingly, these pipeline components may have an increase in their service life.

Analytical Four-Dimensional Ensemble Variational Data Assimilation for Joint State and Parameter Estimation

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

Impact of 4D-Var data assimilation on modelling of the East China Sea dynamics

In this work, the four-dimensional variational (4D-Var) data assimilation (DA) of the Regional Ocean Modelling System (ROMS) is applied in the East China Sea (ECS). The unique capability of optimizing the initial condition (IC), boundary condition (BC) and surface forcing (FC) in ROMS 4D-Var facilitate the simulation of dynamical processes associated with both local and remote forcing. The assimilated data in this study include sea surface temperature (SST), sea surface height (SSH), in situ temperature and salinity profiles, as well as surface drifters and a surface ocean current analysis (OSCAR). Overall, 4D-Var performs well in reducing model-data misfit for all observation types. As tidal forcing plays important roles in the shelf circulations of the ECS, tidal forcing was included in 4D-Var and its impact was evaluated by comparing two experiments with and without tides. The biases of SST in DA analyses are small on the continental shelf in both experiments. However, compared with experiments with tides, the absence of tidal forcing will make temperature higher near the surface layer and lower below mixed layer in the background simulation (3-day forecast using DA analyses as IC) in the warm season of 2014. The difference in temperature profile is associated with two factors: stratification and tidal mixing. The relative importance of the two factors varies with depth.With the aid of the adjoint model, the impacts on the Kuroshio volume transport (KVT) and the Kuroshio onshore intrusion (KOI) contributed by different types of observations are evaluated, as well as the contributions of IC, BC and FC. SSH, SST and in situ temperatures have large total impacts while in situ temperatures have the largest impact per datum. The geographical distributions of observation impacts are similar for different observation types. Large observation impacts extend along the Kuroshio path from the northeast of Taiwan to the southwest of Japan. Several factors control the geographical distribution, which include the model forecast skills, the dynamic processes that are responsible for the transferring of assimilated information, and the specified error covariance. Tracking how the assimilated information propagate in space helps to advance the understanding of the dynamics of KVT and KOI.

GOURSAT PROBLEM FOR THE ADJOINT MODEL TELEGRAPH EQUATION WITH THE RATE a(s, t) IN THE UPPER HALF-PLANE

In the upper half-plane, the classical solution and correctness criterion of the Goursat problem for a linear inhomogeneous adjoint model telegraph equation with variable rate a(s,t) are found explicitly. An explicit formula is obtained for the classical solution of this Goursat problem, unique and stable with respect to the right hand side of the equation and Goursat data. This formula contains implicit characteristic functions of the equation. In the case of a homogeneous conjugate model telegraph equation, the classical solution of this Goursat problem is the Riemann function in all linear mixed (initial-boundary) problems for an inhomogeneous model telegraph equation with variable rate a(s,t). This Riemann function has been calculated by us. A correctness criterion according to Hadamard (necessary and sufficient conditions) of its unique and stable on the right-hand side of the equation and the Goursat data solvability is found. This criterion consists of smoothness requirements on the righthand side of the equation and two Goursat data. The smoothness requirements on the right side of the equation are the condition of continuity of the right-side and the corresponding integral smoothness conditions on the right side of the equation and on the Goursat data – their twice continuous differentiability in the upper half-plane.

Assimilating Near-Surface Wind Retrievals from High-Frequency Radars

Abstract High-frequency radars (HFR) are traditionally used in coastal environments to observe ocean current and wave characteristics. With an HFR forward model, HFR adjoint model, and the Simulating Waves Nearshore model, HFR Doppler spectra observations were used to estimate near-surface winds in the Southern California Bight in October 2017. The HFR 10-m wind retrievals were assimilated into the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) with the COAMPS four-dimensional variational (4DVar) assimilation system to integrate the HFR wind retrievals into the initial conditions. Impact of the HFR-derived winds on the forecast are evaluated in terms of adjoint-derived forecast sensitivity observation impact (FSOI), and by an observing system experiment that compared forecasts from simulations that assimilated the HFR wind retrievals to a control simulation that excluded HFR winds. The addition of the HFR-estimated wind observations reduced the error in the forecasted dry energy norm in the lowest model level and also contributed to small improvements in the 10-m wind field over a 25-day experiment. The potential benefit of this new method to estimate near-surface ocean winds near the coast for data assimilation and improved numerical weather prediction is an exciting advancement in remote sensing of coastal winds and expands the benefit of existing HFR networks beyond their intended use. More importantly, wind fields retrieved from HFR have the potential to fill an observation gap near the shoreline where ship and buoy observations are sparse and scatterometer observations are unavailable due to land contamination.

Active Learning for Well Control Optimization with Surrogate Models

SummaryOptimization of well controls in waterflooding operations has been established as an effective strategy to increase oil recovery efficiency and to reduce operating costs. Optimization problems, however, entail hundreds of full-scale reservoir simulation runs, which can be computationally expensive and impractical for field-scale applications. Fit-for-purpose surrogate models present more efficient alternatives that can be deployed for faster implementation and to enable real-time applications. In recent years, machine learning (ML)-based surrogate models have gained traction in building efficient proxy models to facilitate reservoir engineering and management workflows. For high-dimensional control variables that are frequently encountered in life cycle optimization, gradient-based local search methods have proven to be the optimization algorithms of choice, especially when adjoint models are available to provide the required gradient information in a computationally efficient manner. The use of local search optimization techniques implies that the surrogate models should be locally accurate and adapted to the optimization path that is traversed during the iterations. The adaptation can be accomplished through active learning, where the training of the surrogate model is performed online (throughout the iterations) and tied to the optimization iterations. This paper presents an active learning framework that is tuned to the local search nature of the optimization problem by updating an initially trained surrogate model based on new samples that are generated during the optimization iterations. Specifically, at each iteration, the full reservoir simulation model is performed to evaluate the true objective function and provide the new simulated data to update the surrogate model, thereby enhancing its local prediction accuracy. As the optimization progresses, older samples that become less relevant to the solution at the current iteration are dropped to preserve the local nature of the surrogate model. Various aspects of designing an active learning-based proxy model for well control optimization are discussed and the framework is applied to waterflooding problems to demonstrate its efficiency and superior performance compared to the traditional offline training approach.

Integrating Recurrent Neural Networks With Data Assimilation for Scalable Data‐Driven State Estimation

AbstractData assimilation (DA) is integrated with machine learning in order to perform entirely data‐driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as pretrained surrogate models to replace key components of the DA cycle in numerical weather prediction (NWP), including the conventional numerical forecast model, the forecast error covariance matrix, and the tangent linear and adjoint models. It is shown how these RNNs can be initialized using DA methods to directly update the hidden/reservoir state with observations of the target system. The results indicate that these techniques can be applied to estimate the state of a system for the repeated initialization of short‐term forecasts, even in the absence of a traditional numerical forecast model. Further, it is demonstrated how these integrated RNN‐DA methods can scale to higher dimensions by applying domain localization and parallelization, providing a path for practical applications in NWP.

Development of GRAPES-CUACE adjoint model version 2.0 and its application in sensitivity analysis of ozone pollution in north China

We presented the development of the gaseous chemistry adjoint module of the meteorological-chemical model system GRAPES-CUACE (Global/Regional Assimilation and PrEdiction System coupled with CMA Unified Atmospheric Chemistry Environmental Forecasting System) on the basis of the previously constructed aerosol adjoint module. The latest version of the GRAPES-CUACE adjoint model mainly includes the adjoint of the physical and chemical processes, the adjoint of the transport processes, and the adjoint of interface programs, of both gas and aerosol. The adjoint implementation was validated for the full model, and adjoint results showed good agreement with brute force sensitivities. We also applied the newly developed adjoint model to the sensitivity analysis of an ozone episode occurred in Beijing on July 2, 2017, as well as the design of emission-reduction strategies for this episode. The relationships between the ozone concentration and precursor emissions were well captured by the adjoint model. It is indicated that for a case used here, the Beijing peak ozone concentration was influenced mostly by local emissions (6.2–24.3%), as well as by surrounding emissions, including Hebei (4.4–16.8%), Tianjin (1.8–6.6%), Shandong (1.8–2.6%), and Shanxi (<1%). In addition, reduction of NOx, VOCs, and CO emissions in these regions would effectively decrease the Beijing peak ozone concentration. This study highlights the capability of GRAPES-CUACE adjoint model in quantifying “emission-concentration” relationship and in providing guidance for environmental control policy.

A Framework for Four-Dimensional Variational Data Assimilation Based on Machine Learning.

The initial field has a crucial influence on numerical weather prediction (NWP). Data assimilation (DA) is a reliable method to obtain the initial field of the forecast model. At the same time, data are the carriers of information. Observational data are a concrete representation of information. DA is also the process of sorting observation data, during which entropy gradually decreases. Four-dimensional variational assimilation (4D-Var) is the most popular approach. However, due to the complexity of the physical model, the tangent linear and adjoint models, and other processes, the realization of a 4D-Var system is complicated, and the computational efficiency is expensive. Machine learning (ML) is a method of gaining simulation results by training a large amount of data. It achieves remarkable success in various applications, and operational NWP and DA are no exception. In this work, we synthesize insights and techniques from previous studies to design a pure data-driven 4D-Var implementation framework named ML-4DVAR based on the bilinear neural network (BNN). The framework replaces the traditional physical model with the BNN model for prediction. Moreover, it directly makes use of the ML model obtained from the simulation data to implement the primary process of 4D-Var, including the realization of the short-term forecast process and the tangent linear and adjoint models. We test a strong-constraint 4D-Var system with the Lorenz-96 model, and we compared the traditional 4D-Var system with ML-4DVAR. The experimental results demonstrate that the ML-4DVAR framework can achieve better assimilation results and significantly improve computational efficiency.

Optimal Precursors Identification for North Atlantic Oscillation Using the Parallel Intelligence Algorithm

The North Atlantic Oscillation (NAO) with abnormal sea level pressure (SLP) differences influence the westerly wind strength and storm tracks in the North Atlantic, which further affects the winter climate in the northern hemisphere. The predictability of NAO has become an important area of climate research in recent years. The identification of optimal precursors (OPRs) would help to investigate the dynamics of atmospheric and oceanic motions, as well as the nonlinear characteristic. The conditional nonlinear optimal perturbation (CNOP) method has been widely used in research on the OPR of the climatic event to explore which kind of initial perturbation is most likely to trigger climate events. However, the previous works on NAO’s OPR are based on a simple ideal model, which cannot describe the evolution process of NAO. Moreover, the commonly used algorithms that rely on the adjoint model are not suitable for the large complicated numerical models that do not have corresponding adjoint models, like Community Earth System Model (CESM). To break through the limitation, this paper proposes the parallel principal component analysis (PCA)-based particle swarm optimization (PSO) and genetic algorithm (GA) hybrid algorithm (PGAPSO) algorithm to identify the OPR of NAO using CESM. For different initial conditions, OPRs identified by the proposed method can always make the basic state develop into NAO events with corresponding phases. Compared with other adjoint-free approaches, the proposed method has relatively better fitness values and more mature patterns. The results also reveal that the proposed method can avoid falling into a local optimum and has strong robustness. In terms of performance, the proposed method searches in feature space with a much lower number of dimensions, thus improving efficiency. In addition, the proposed method is accelerated with multiple parallel frameworks to enhance performance, and it achieves the speedup ratio of 40.2.

Adjoint Waveform Tomography of South America

AbstractWe used 3D spectral‐element seismic wave simulations and data from 112 earthquakes and 1,311 seismic stations, totalizing 20,884 unique ray paths, to construct an adjoint waveform tomographic model of South America. We performed 23 conjugate‐gradient iterations using exponentiated phase (EP) measurements. Our final model (SAAM23, South American Adjoint Model—iteration 23) shows a 50% decrease in the EP misfit relative to its 3D starting model. We further assessed the phase misfit reduction by using cross‐correlation travel‐time measurements of 53 earthquakes not included in the inversion. We estimated SAAM23 resolution using point‐spread function tests and density coverage analysis. The Nazca Slab is well imaged and is shown to be continuous in the 300–500 km depth range. Beneath northern South America, the slab traverses the mantle transition zone and continues into the lower mantle. In the central and southern part of South America, the slab appears to flatten near the 650 km discontinuity before continuing into the lower mantle. In the stable Precambrian platform, both cratons (Amazonian and São Francisco), as well as covered cratonic blocks beneath the intracratonic Paraná and Parnaíba basins (Paranapanema and Parnaíba, respectively), show high velocities at lithospheric depths. The seismic Lithosphere/Asthenosphere boundary (LAB) agrees well with published values obtained by S‐wave receiver functions. In the Amazonian craton, the positive lithospheric S‐wave velocity anomalies and LAB depth increase with the average age of the geochronological provinces. No lithospheric high‐velocity anomalies were found beneath the Río de la Plata Craton.

Sector‐Based Top‐Down Estimates of NOx, SO2, and CO Emissions in East Asia

Top‐down estimates using satellite data provide important information on the sources of air pollutants. We develop a sector‐based 4D‐Var framework based on the GEOS‐Chem adjoint model to address the impacts of co‐emissions and chemical interactions on top‐down emission estimates. We apply OMI NO2, OMI SO2, and MOPITT CO observations to estimate NO x , SO2, and CO emissions in East Asia during 2005–2012. Posterior evaluations with surface measurements show reduced normalized mean bias (NMB) by 7% (NO2)–15% (SO2) and normalized mean square error (NMSE) by 8% (SO2)–9% (NO2) compared to a species‐based inversion. This new inversion captures the peak years of Chinese SO2 (2007) and NO x (2011) emissions and attributes their drivers to industry and energy activities. The CO peak in 2007 in China is driven by residential and industry emissions. In India, the inversion attributes NO x and SO2 trends mostly to energy and CO trend to residential emissions.

How well can inverse analyses of high-resolution satellite data resolve heterogeneous methane fluxes? Observing system simulation experiments with the GEOS-Chem adjoint model (v35)

Abstract. We perform observing system simulation experiments (OSSEs) with the GEOS-Chem adjoint model to test how well methane emissions over North America can be resolved using measurements from the TROPOspheric Monitoring Instrument (TROPOMI) and similar high-resolution satellite sensors. We focus analysis on the impacts of (i) spatial errors in the prior emissions and (ii) model transport errors. Along with a standard scale factor (SF) optimization we conduct a set of inversions using alternative formalisms that aim to overcome limitations in the SF-based approach that arise for missing sources. We show that 4D-Var analysis of the TROPOMI data can improve monthly emission estimates at 25 km even with a spatially biased prior or model transport errors (42 %–93 % domain-wide bias reduction; R increases from 0.51 up to 0.73). However, when both errors are present, no single inversion framework can successfully improve both the overall bias and spatial distribution of fluxes relative to the prior on the 25 km model grid. In that case, the ensemble-mean optimized fluxes have a domain-wide bias of 77 Gg d−1 (comparable to that in the prior), with spurious source adjustments compensating for the transport errors. Increasing observational coverage through longer-timeframe inversions does not significantly change this picture. An inversion formalism that optimizes emission enhancements rather than scale factors exhibits the best performance for identifying missing sources, while an approach combining a uniform background emission with the prior inventory yields the best performance in terms of overall spatial fidelity – even in the presence of model transport errors. However, the standard SF optimization outperforms both of these for the magnitude of the domain-wide flux. For the common scenario in which prior errors are non-random, approximate posterior error reduction calculations (derived via gradient-based randomization) for the inversions reflect the sensitivity to observations but have no spatial correlation with the actual emission improvements. This demonstrates that such information content analysis can be used for general observing system characterization but does not describe the spatial accuracy of the posterior emissions or of the actual emission improvements. Findings here highlight the need for careful evaluation of potential missing sources in prior emission datasets and for robust accounting of model transport errors in inverse analyses of the methane budget.

SphGLLTools: A toolbox for visualization of large seismic model files based on 3D spectral-element meshes

Adjoint tomography, a full-waveform inversion technique based on 3D wave simulations, has become a commonly used tool in passive-source seismology, drawing on advances in computational power and numerical methods. From global to reservoir scales, seismic models can iteratively be updated in adjoint inversions by extracting information from full seismic waveforms. Seismic models are typically constructed on the numerical mesh used for wave simulations. Thus the size of model files depends on the minimum resolvable period achieved in simulations controlled by the numerical mesh (the higher the mesh resolution, the larger the model and mesh files). This is specifically a concern for recent global-scale adjoint tomographic models where the size and format of numerical meshes pose challenges for model visualization, analysis, interpretation, and sharing model files. Here, we present SphGLLTools, an open-source toolbox that intends to diminish these challenges by expanding global adjoint models onto spherical harmonic functions, which are widely used in global seismology. Our tools are initially designed for spectral-element meshes used in recent global adjoint tomography studies. SphGLLTools facilitate many commonplace tasks for model visualization and analysis, including spherical harmonic expansion of models sampled on spectral-element meshes together with associated tools for easy sharing, visualization, and interpretation of large-scale seismic model files. All the developed routines are accompanied by user instructions and are available through GitHub. For transparency, reproducibility, and educational purposes, we also include Colab notebooks, which provide an intuitive and comprehensive review of the principles and methods for spectral-element meshes, spherical harmonic expansion, and other model analysis tools.

The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-CASAM-L): I. Mathematical Framework

This work presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is conceived for obtaining the exact expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters (including boundary and initial conditions) underlying the respective forward/adjoint systems. Since many of the most important responses for linear systems involve the solutions of both the forward and the adjoint linear models that correspond to the respective physical system, the sensitivity analysis of such responses makes it necessary to treat linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator admits an adjoint operator). The nth-CASAM-L determines the exact expression of arbitrarily-high order sensitivities of responses to the parameters underlying both the forward and adjoint models of a nonlinear system, thus enable the most efficient and accurate computation of such sensitivities. The mathematical framework underlying the nth-CASAM is developed in linearly increasing higher-dimensional Hilbert spaces, as opposed to the exponentially increasing “parameter-dimensional” spaces in which response sensitivities are computed by other methods, thus providing the basis for overcoming the “curse of dimensionality” in sensitivity analysis and all other fields (uncertainty quantification, predictive modeling, etc.) which need such sensitivities. In particular, for a scalar-valued valued response associated with a nonlinear model comprising TP parameters, the 1st-−CASAM-L requires 1 additional large-scale adjoint computation (as opposed to TP large-scale computations, as required by other methods) for computing exactly all of the 1st-−order response sensitivities. All of the (mixed) 2nd-order sensitivities are computed exactly by the 2nd-CASAM-L in at most TP computations, as opposed to TP(TP + 1)/2 computations required by all other methods, and so on. For every lower-order sensitivity of interest, the nth-CASAM-L computes the “TP next-higher-order” sensitivities in one adjoint computation performed in a linearly increasing higher-dimensional Hilbert space. Very importantly, the nth-CASAM-L computes the higher-level adjoint functions using the same forward and adjoint solvers (i.e., computer codes) as used for solving the original forward and adjoint systems, thus requiring relatively minor additional software development for computing the various-order sensitivities.

Estimating NOx LOTOS-EUROS CTM Emission Parameters over the Northwest of South America through 4DEnVar TROPOMI NO2 Assimilation

In this work, we present the development of a 4D-Ensemble-Variational (4DEnVar) data assimilation technique to estimate NOx top-down emissions using the regional chemical transport model LOTOS-EUROS with the NO2 observations from the TROPOspheric Monitoring Instrument (TROPOMI). The assimilation was performed for a domain in the northwest of South America centered over Colombia, and includes regions in Panama, Venezuela and Ecuador. In the 4DEnVar approach, the implementation of the linearized and adjoint model are avoided by generating an ensemble of model simulations and by using this ensemble to approximate the nonlinear model and observation operator. Emission correction parameters’ locations were defined for positions where the model simulations showed significant discrepancies with the satellite observations. Using the 4DEnVar data assimilation method, optimal emission parameters for the LOTOS-EUROS model were estimated, allowing for corrections in areas where ground observations are unavailable and the region’s emission inventories do not correctly reflect the current emissions activities. The analyzed 4DEnVar concentrations were compared with the ground measurements of one local air quality monitoring network and the data retrieved by the satellite instrument Ozone Monitoring Instrument (OMI). The assimilation had a low impact on NO2 surface concentrations reducing the Mean Fractional Bias from 0.45 to 0.32, primordially enhancing the spatial and temporal variations in the simulated NO2 fields.

Adjoint model for estimating material parameters based on microstructure evolution during spinodal decomposition

Data assimilation techniques are attracting increasing attention because they enable researchers to estimate material parameters by integrating an advanced computational model with experimental data of microstructure evolution. In this study, we develop an adjoint model to integrate a phase-field model for spinodal decomposition with time-series measurement data of compositional field maps to estimate the unknown parameters in the phase-field model. As a case study, simultaneous estimation of six parameters (Gibbs energy parameters, gradient energy coefficient, etc.) in the phase-field model is considered. To confirm the effectiveness of the developed adjoint model, numerical tests called ``twin experiments'' are conducted using synthetic measurement data prepared in advance through phase-field simulation. In the twin experiments, the optimum estimates of six model parameters of interest are shown to coincide with true values, indicating that several model parameters can be successfully estimated. Furthermore, the effects of the standard deviation of measurement noise $(\ensuremath{\sigma})$ and the time interval of measurements $(\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}})$ on uncertainties of optimum estimates of parameters $({\ensuremath{\sigma}}^{\mathrm{est}})$ are examined by conducting twin experiments. It is shown that there is a positive correlation between $\ensuremath{\sigma}$ and ${\ensuremath{\sigma}}^{\mathrm{est}}$ or between $\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}}$ and ${\ensuremath{\sigma}}^{\mathrm{est}}$, which is essential information for designing experiments to estimate model parameters. The developed adjoint model is assumed to be useful for estimating unknown parameters (e.g., Gibbs energy parameters of a nonequilibrium phase) using time-series measurement data of microstructure evolution during spinodal decomposition.

Nonlocal Population Sources Triggering Dinoflagellate Blooms in the Changjiang Estuary and Adjacent Seas: A Modeling Study

AbstractDinoflagellates frequently cause harmful, large‐scale spring algal blooms in the Changjiang Estuary and adjacent seas of China. However, the population source of some dinoflagellates in this area remains unknown. We deployed an adjoint model and a coupled physical‐biological model to explore the possible nonlocal dinoflagellate population sources to the Changjiang Estuary and adjacent seas. Our simulation results revealed that the Taiwan Strait and the area east of Taiwan are two nonlocal source regions of May dinoflagellate blooms in the study area. Under different hydrodynamic and biochemical conditions, dinoflagellates from the Taiwan Strait directly triggered dinoflagellate blooms from south to north along the coast of China. Dinoflagellates from the area east of Taiwan first concentrated and bred in the offshore temperature frontal area and then spread southwestward, triggering dinoflagellate blooms along the Zhejiang coast. Due to the different influence mechanisms, it took longer for the initial dinoflagellate population in the Taiwan Strait to exert the same impact on dinoflagellate blooms in the study area as that from the area east of Taiwan. Moreover, the density and appearance time of the initial dinoflagellate population in the Taiwan Strait affected their biomass and bloom range in the study area. Even a small initial dinoflagellate population east of Taiwan could trigger a bloom in the study area. This study suggests the target domains for finding nonlocal dinoflagellate cysts and provides a strategy to predict dinoflagellate blooms in the Changjiang Estuary adjacent area by monitoring dinoflagellate biomass in the nonlocal source regions.

Augmented NETT regularization of inverse problems

We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces regularity in the encoder domain, augmented by a penalty that penalizes the distance to the signal manifold. We present a rigorous convergence analysis including stability estimates and convergence rates. For that purpose, we prove the coercivity of the regularizer used without requiring explicit coercivity assumptions for the networks involved. We propose a possible realization together with a network architecture and a modular training strategy. Applications to sparse-view and low-dose CT show that aNETT achieves results comparable to state-of-the-art deep-learning-based reconstruction methods. Unlike learned iterative methods, aNETT does not require repeated application of the forward and adjoint models during training, which enables the use of aNETT for inverse problems with numerically expensive forward models. Furthermore, we show that aNETT trained on coarsely sampled data can leverage an increased sampling rate without the need for retraining.