Inverse Transport Research Articles

Nonlinear Inverse Optimal Transport: Identifiability of the Transport Cost from Its Marginals and Optimal Values

Nonlinear Inverse Optimal Transport: Identifiability of the Transport Cost from Its Marginals and Optimal Values

Inverse Rendering for Tomographic Volumetric Additive Manufacturing

Tomographic Volumetric Additive Manufacturing (TVAM) is an emerging 3D printing technology that can create complex objects in under a minute. The key idea is to project intense light patterns onto a rotating vial of photo-sensitive resin, causing polymerization where the cumulative dose of these patterns reaches the polymerization threshold. We formulate the pattern calculation as an inverse light transport problem and solve it via physically based differentiable rendering. In doing so, we address longstanding limitations of prior work by accurately modeling and correcting for scattering in composite resins, printing in non-symmetric vials, and supporting unusual printing geometries. We also introduce an improved discretization scheme that exploits the ray tracing operation to mitigate resolution-related artifacts in prints. We demonstrate the benefits of our method in real-world experiments, where our computed patterns produce prints with an improved fidelity.

ScConfluence: single-cell diagonal integration with regularized Inverse Optimal Transport on weakly connected features

The abundance of unpaired multimodal single-cell data has motivated a growing body of research into the development of diagonal integration methods. However, the state-of-the-art suffers from the loss of biological information due to feature conversion and struggles with modality-specific populations. To overcome these crucial limitations, we here introduce scConfluence, a method for single-cell diagonal integration. scConfluence combines uncoupled autoencoders on the complete set of features with regularized Inverse Optimal Transport on weakly connected features. We extensively benchmark scConfluence in several single-cell integration scenarios proving that it outperforms the state-of-the-art. We then demonstrate the biological relevance of scConfluence in three applications. We predict spatial patterns for Scgn, Synpr and Olah in scRNA-smFISH integration. We improve the classification of B cells and Monocytes in highly heterogeneous scRNA-scATAC-CyTOF integration. Finally, we reveal the joint contribution of Fezf2 and apical dendrite morphology in Intra Telencephalic neurons, based on morphological images and scRNA.

Forward and inverse river contaminant transport modeling using group preserving scheme

Environmental concerns have necessitated the development of computational models predicting pollutant dispersion in natural water systems. Due to the ill-posed nature of the inverse contaminant transport equation, solving this equation using all stable and convergent inverse methods is impossible. Factors such as river geometry, unsteady and non-uniform flow, and tidal influences add to the complexity of the inverse problem. These factors have prompted the evaluation of Group Preserving Scheme for environmental applications. The inverse solution method derives a general equation for solving ordinary differential equations by addressing a dynamical system at negative time steps, ensuring convergence. Three test cases have been presented to evaluate Backward Group Preserving Scheme (BGPS). These have included validation using observational data from Missouri River, inverse simulation in a tidal river, and sensitivity analysis of parameters such as pollutant patterns, advection, dispersion, and decay coefficients. The dataset includes calibrated data from Missouri River, which demonstrated high accuracy, with Mean Relative Error (MRE) ranging from 2.8% to 5.0% for the inverse model. Under tidal conditions, accuracy decreases over time but remains robust, with a Nash–Sutcliffe efficiency of 0.77–0.96 and an MRE of 0.9%–5.9%. Sensitivity analysis revealed optimal model performance for Péclet numbers greater than 500. The model performed best with gradual, wide-peaked pollutant patterns and moderate decay rates (Damköhler number between 5 and 10). BGPS proves effective for transport simulation and concentration history reconstruction in complex rivers, including those with tidal influences, offering a robust tool for water contamination analysis in various flow conditions.

Inverse pH Gradient-Assay for Facile Characterization of Proton-Antiporters in Xenopus Oocytes.

Xenopus oocytes represent one of the most versatile model systems for characterizing the properties of membrane transporters. However, for studying proton-coupled antiporters, the use of Xenopus oocytes has so far been limited to so-called injection-based transport assays. In such assays, where the compound is injected directly into the oocytes' cytosol and transport is detected by monitoring substrate efflux, poor control over internal diffusion and concentration are incompatible with mechanistic characterizations. In this study, we present an inverse pH-gradient transport assay. Herein, an outward-facing proton gradient enables the characterization of proton antiporters via facile import-based transport assays. We describe two approaches for establishing sustained outward-facing proton gradients across the oocyte membrane, namely by applying alkaline external conditions or through surprisingly stable carbonyl cyanide m-chlorophenyl-hydrazone (CCCP)-mediated acidification of the cytosol. Previously, genetic evidence has shown that DTX18 from Arabidopsis thaliana is essential for the deposition of the hydroxycinnamic acid amide p-coumaroylagmatine (coumaroylagmatine) defence compound on the leaf surface. However, direct evidence for its ability to transport coumarol-agmatine has not been provided. Here, using Xenopus oocytes as expression hosts, we demonstrate DTX18's ability to transport coumaroyl-agmatine via both injection-based and inverse pH-gradient transport assays. Notably, by showing that DTX18 is capable of accumulating its substrate against its concentration gradient, we showcase the compatibility of the latter with mechanistic investigations.

Source term estimation for continuous plume dispersion in Fusion Field Trial-07: Bayesian inference probability adjoint inverse method

In scenarios involving sudden releases of unidentified gases or concealed pollution emergencies, source control emerges as a critical procedure to safeguard residential air quality. Appropriate inverse source tracking methodology depending on diverse measurement data could be utilized to promptly identify pollutant source parameters. In this study, source term estimation (STE) method, i.e., jointly combining probability adjoint method with the Bayesian inference method, has been proposed. General form of the pollutant inverse transport equation was firstly established. Subsequently, the pollution source information, assumed from single continuous point releases during Fusion Field Trials 2007 under an unsteady wind field, was identified using the Bayesian inference probability adjoint inverse method. Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) and Differential Evolution Markov Chain Monte Carlo (DE-MCMC) were then compared as sampling methods for Bayesian inference. Results indicated that the DE-MCMC algorithm has superior convergence and could present higher accuracy of pollutant source information than that of MH-MCMC algorithm, particularly for highly nonlinear and multi-modal distribution systems. Furthermore, the integration of Union standard Adjoint Location Probability (UALP) as prior information into the Bayesian inference probability adjoint inverse method effectively narrowed the sampling range, enhancing both the accuracy and robustness of the proposed approach. Finally, the impact of the covariance matrix on the inverse identification accuracy was explored. Overall, this research has provided insights into the future applicability of this Bayesian inference inversion technique for point source identification.

Inverse aqueous transport modeling for emergency response

Inverse aqueous transport modeling for emergency response

Unmanned aerial vehicle observations of the vertical distribution of particulate matter and sulfur dioxide at a regional background site in northwest China

The vertical measurements of atmospheric pollutants are essential for understanding various atmospheric chemical processes and the transmission of air pollutants. Herein, we measured particulate matter (PM) and SO2 concentrations using a six-axis unmanned aerial vehicle (UAV) equipped with portable monitors at the Akedala Background Station in northwest China from the surface to 500 m above the ground level. Twelve-day measurements (68 flights) were conducted from July 13 to 24, 2020. Results showed that the UAV platform could effectively capture the vertical distribution of PM and SO2. During the observation period, the concentrations of PM1, PM2.5, and PM10 in Akedala were 0.1–11.8, 0.2–13.0, and 0.2–21.7 μg/m3, respectively, and SO2 concentrations ranged between 0.1 and 29.4 ppb. The weather condition and backward trajectory indicated that the air mass affecting the station mainly originates from Kazakhstan, southern Russia, and northern Xinjiang.PM and SO2 can be classified into different types based on their vertical profile characteristics, where SO2 mainly showed an incremental distribution, which may be related to the long-distance transport of pollutants. PM mainly showed unimodal distributions, which may be related to the inverse temperature phenomenon and transport of pollutants. Remote sensing data and MIX emission inventory showed the presence of dot emission areas in southern Russia, Kazakhstan, and northern Xinjiang cities, which made important contributions to the air pollutants in Akedala.

Double-banded topology valley transport

The advent of topology theory has facilitated the emergence of unique physical properties in engineered structures, garnering significant interest and investigation. This paper presents a phonon crystal design approach predicated on the Valley Hall effect, capable of achieving energy band inversion and topological valley transport across various frequency ranges. By merely rotating the scatterer, multiple coexisting linear Dirac points at the Brillouin zone K point can be disrupted, giving rise to bandgaps exhibiting distinct topological characteristics. Reversing the rotation direction simultaneously alters the vortex chirality. This inherent property lays the foundation for topological valley transport. Furthermore, this paper examines the two-band valley transport attributes of phonon crystals with diverse transmission routes. To explore the applicability of the designed phonon crystal in topological acoustics, a two-band acoustic splitter is employed to investigate topological transport behavior. Simulation outcomes demonstrate exceptional transport performance. This study offers novel insights for sound wave control design and bears potential applicability to multifunctional acoustic devices such as acoustic sensors, acoustic signal processing, and acoustic communication.

Large-scale arsenic mobilization from legacy sources in anoxic aquifers: Multiple methods and multi-decadal perspectives

While geogenic arsenic (As) contamination of aquifers have been intensively investigated across the world, the mobilization and transport of As from anthropogenic sources have received less scientific attention, despite emerging evidence of poor performance of widely used risk assessment models. In this study we hypothesize that such poor model performance is largely due to insufficient attention to heterogeneous subsurface properties, including the hydraulic conductivity K and the solid-liquid partition (Kd), as well as neglect of laboratory-to-field scaling effects. Our multi-method investigation includes i) inverse transport modelling, ii) in-situ measurements of As concentrations in paired samples of soil and groundwater, and iii) batch equilibrium experiments combined with (iv) geochemical modelling. As case study we use a unique 20-year series of spatially distributed monitoring data, capturing an expanding As plume in a Chromated Copper Arsenate (CCA)-contaminated anoxic aquifer in southern Sweden. The in-situ results showed a high variability in local Kd values of As (1 to 107 L kg−1), implying that over-reliance of data from only one or few locations can lead to interpretations that are inconsistent with field-scale As transport. However, the geometric mean of the local Kd values (14.4 L kg−1) showed high consistency with the independently estimated field-scale “effective Kd” derived from inverse transport modelling (13.6 L kg−1). This provides empirical evidence for the relevance of using geometric averaging when estimating large-scale “effective Kd” values from local measurements within highly heterogenous, isotropic aquifers. Overall, the considered As plume is prolonged by about 0.7 m year−1, now starting to extend beyond the borders of the industrial source area, a problem likely shared with many of the world's As-polluted sites. In this context, geochemical modelling assessments, as presented here, provided a unique understanding of the processes governing As retention, including local variability in, e.g., Fe/Al-(hydr)oxides contents, redox potential and pH.

Ensemble physics informed neural networks: A framework to improve inverse transport modeling in heterogeneous domains

Modeling fluid flow and transport in heterogeneous systems is often challenged by unknown parameters that vary in space. In inverse modeling, measurement data are used to estimate these parameters. Due to the spatial variability of these unknown parameters in heterogeneous systems (e.g., permeability or diffusivity), the inverse problem is ill-posed and infinite solutions are possible. Physics-informed neural networks (PINN) have become a popular approach for solving inverse problems. However, in inverse problems in heterogeneous systems, PINN can be sensitive to hyperparameters and can produce unrealistic patterns. Motivated by the concept of ensemble learning and variance reduction in machine learning, we propose an ensemble PINN (ePINN) approach where an ensemble of parallel neural networks is used and each sub-network is initialized with a meaningful pattern of the unknown parameter. Subsequently, these parallel networks provide a basis that is fed into a main neural network that is trained using PINN. It is shown that an appropriately selected set of patterns can guide PINN in producing more realistic results that are relevant to the problem of interest. To assess the accuracy of this approach, inverse transport problems involving unknown heat conductivity, porous media permeability, and velocity vector fields were studied. The proposed ePINN approach was shown to increase the accuracy in inverse problems and mitigate the challenges associated with non-uniqueness.

Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that maximize the expected information gain (EIG) in the solution of the underlying Bayesian inverse problem. Computation of the EIG is usually prohibitive for PDE-based OED problems. To make the evaluation of the EIG tractable, we approximate the (PDE-based) parameter-to-observable map with a derivative-informed projected neural network (DIPNet) surrogate, which exploits the geometry, smoothness, and intrinsic low-dimensionality of the map using a small and dimension-independent number of PDE solves. The surrogate is then deployed within a greedy algorithm-based solution of the OED problem such that no further PDE solves are required. We analyze the EIG approximation error in terms of the generalization error of the DIPNet and show they are of the same order. Finally, the efficiency and accuracy of the method are demonstrated via numerical experiments on OED problems governed by inverse scattering and inverse reactive transport with up to 16,641 uncertain parameters and 100 experimental design variables, where we observe up to three orders of magnitude speedup relative to a reference double loop Monte Carlo method.

Constraining CaCO3 Export and Dissolution With an Ocean Alkalinity Inverse Model

AbstractOcean alkalinity plays a fundamental role in the apportionment of CO2 between the atmosphere and the ocean. The primary driver of the ocean's vertical alkalinity distribution is the formation of calcium carbonate (CaCO3) by organisms at the ocean surface and its dissolution at depth. This so‐called “CaCO3 counterpump” is poorly constrained, however, both in terms of how much CaCO3 is exported from the surface ocean, and at what depth it dissolves. Here, we created a steady‐state model of global ocean alkalinity using Ocean Circulation Inverse Model transport, biogeochemical cycling, and field‐tested calcite and aragonite dissolution kinetics. We find that limiting CaCO3 dissolution to below the aragonite and calcite saturation horizons cannot explain excess alkalinity in the upper ocean, and that models allowing dissolution above the saturation horizons best match observations. Linking dissolution to organic matter respiration, or imposing a constant dissolution rate both produce good model fits. Our best performing models require export between 1.1 and 1.8 Gt PIC y−1 (from 73 m), but all converge to 1.0 Gt PIC y−1 export at 279 m, indicating that both high‐ and low‐export scenarios can match observations, as long as high export is coupled to high dissolution in the upper ocean. These results demonstrate that dissolution is not a simple function of seawater CaCO3 saturation (Ω) and calcite or aragonite solubility, and that other mechanisms, likely related to the biology and ecology of calcifiers, must drive significant dissolution throughout the water column.

Comment on ‘Geophysical inversion and optimal transport’ by M. Sambridge, A. Jackson and A. P. Valentine

SUMMARY A similarity measure between waveforms developed by Sambridge et al. realized an effective use of optimal transport as well as computational efficiency through the marginalization of a 2-D probability distribution obtained from a seismogram. We demonstrate that information loss due to marginalization could lead to significant non-uniqueness in the resulting measure and propose the use of the sliced Wasserstein distance as a potential solution. This formulation may enhance the robustness of the method developed by Sambridge et al. by maintaining its computational efficiency.

Reply to comment on Geophysical inversion and Optimal Transport, 231, 172–198, by Okazaki & Ueda

SUMMARY Concerns raised by Okazaki & Ueda (2022) on the paper by Sambridge et al. (2022) are addressed. Two issues are discussed and some new numerical results presented. The first concerns whether the properties of the Wasserstein time-series misfit introduced in our earlier paper will translate to model space non-uniqueness in a seismic waveform inversion setting. It is argued that this is unlikely, given the special conditions, which must exist between all observed/predicted seismic waveform pairs for non-uniqueness to result. The second issue discussed is the efficacy of using the Sliced Wasserstein algorithm of Bonneel et al. (2015) as an alternate to the marginal Wasserstein algorithm, as proposed by Okazaki & Ueda (2022). It is argued that for optimization-based waveform fitting, the Sliced Wasserstein algorithm is a viable alternate provided care is taken to ensure that conditions arise which do invalidate analytical derivative expressions of the resulting Wasserstein misfit. In practice, this would likely mean recasting the 2D Optimal Transport problem posed in our earlier paper onto unstructured grids.

Multi-heterostructured SnO2/SnSx embedded in carbon framework for high-performance sodium-ion storage.

Heterostructure materials, as newborn electrode materials for rechargeable batteries, are attracting increasing attention due to their robust architectures and superior electrochemical performances. It is widely believed that the inner electric field induced at the interface can improve the electric conductivity and ion diffusion kinetics, thus enhancing the long-term stability and high-rate performance of the batteries. Although much progress is made on heterostructure construction, the performance of the batteries is still far from satisfying the commercial applications. In this work, a new type of SnO2/SnSx (x=1, 1.5) heterostructure embedded in carbon framework (C@SnO2/SnSx) is constructed via a facile sulfidation process. Compared to a single heterojunction, the multi-heterojunctions generated at SnO2/SnSx interface can induce an intensified built-in electric field, which promotes charge transportation and reaction kinetics of the electrode for Na-ions storage. Upon the sodiation process, the induced intensified electric field drives Na ions from Sn2S3 or SnO2 to SnS, while an inverse transportation of Na ions are accelerated upon the desodation process. As a result, C@SnO2/SnSx exhibits an outstanding reversible capacity of 510mAhg-1 after 300 cycles at 200mAg-1.

Coupled-decoupled turbulence structures of stable boundary layer during heavy haze pollution events

Heavy haze pollution events are closely related to the turbulent structure of the stable boundary layer (SBL). SBL can be divided into two regimes, weak(coupled) and strong(decoupled). The weak SBL conforms to the classical turbulent theory and couples with the surface and different heights, whereas the strong SBL does not conform and decouples. However, the thresholds between coupled and decoupled SBL have not been determined in haze pollution events. Five levels of turbulence observation data from two severe haze pollution cases observed at the 255 m meteorological tower in Tianjin were employed to address this dilemma. The first case was analyzed in detail, and the second case was used for verification. The occurrence frequency of SBL was approximately 50% during the two haze pollution cases. The wind speed thresholds distinguishing coupled and decoupled SBL are: 2.5 m s−1 at 40 m, 4.0 m s−1 at 80 m, and 5.0 m s−1 at 120 m. The decoupled SBLs accounted for >70% of SBLs in haze pollution events. The turbulent structures notably differed between coupled and decoupled SBL events. In a decoupled SBL, the scalar concentration at different heights was substantially higher, the strength and occurrence frequency of sub-mesoscale motion were larger, and turbulent barrier effects occurred. Moreover, there was an inverse gradient transport and a smaller spatiotemporal scale of turbulent eddies. Therefore, there was a weaker turbulent kinetic energy, flux, and turbulent correlation across the layers in the decoupled SBL. The results reveal the failure of Monin-Obukhov similarity theory and traditional turbulent energy spectrum theory in a decoupled SBL. Wind speed thresholds can be widely used in the severe haze pollution simulation. The results of this study also indicate that decoupled SBL requires further study and attention in haze pollution events to improve the accuracy of pollutant concentration forecasting.

A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients

We study measure-valued solutions of the inhomogeneous continuity equation where the coefficients v and g are of low regularity. A new superposition principle is proven for positive measure solutions and coefficients for which the recently-introduced dynamic Hellinger–Kantorovich energy is finite. This principle gives a decomposition of the solution into curves that satisfy the characteristic system in an appropriate sense. In particular, it provides a generalization of existing superposition principles to the low-regularity case of g where characteristics are not unique with respect to h. Two applications of this principle are presented. First, uniqueness of minimal total-variation solutions for the inhomogeneous continuity equation is obtained if characteristics are unique up to their possible vanishing time. Second, the extremal points of dynamic Hellinger–Kantorovich-type regularizers are characterized. Such regularizers arise, for example, in the context of dynamic inverse problems and dynamic optimal transport.

Contaminant source identification in groundwater by means of artificial neural network

In a desired environmental protection system, groundwater may not be excluded. In addition to the problem of over-exploitation, in total disagreement with the concept of sustainable development, another not negligible issue concerns the groundwater contamination. Mainly, this aspect is due to intensive agricultural activities or industrialized areas. In literature, several papers have dealt with transport problem, especially for inverse problems in which the release history or the source location are identified. The innovative aim of the paper is to develop a data-driven model that is able to analyze multiple scenarios, even strongly non-linear, in order to solve forward and inverse transport problems, preserving the reliability of the results and reducing the uncertainty. Furthermore, this tool has the characteristic of providing extremely fast responses, essential to identify remediation strategies immediately. The advantages produced by the model were compared with literature studies. In this regard, a feedforward artificial neural network, which has been trained to handle different cases, represents the data-driven model. Firstly, to identify the concentration of the pollutant at specific observation points in the study area (forward problem); secondly, to deal with inverse problems identifying the release history at known source location; then, in case of one contaminant source, identifying the release history and, at the same time, the location of the source in a specific sub-domain of the investigated area. At last, the observation error is investigated and estimated. The results are satisfactorily achieved, highlighting the capability of the ANN to deal with multiple scenarios by approximating nonlinear functions without the physical point of view that describes the phenomenon, providing reliable results, with very low computational burden and uncertainty.

Parallel inverse-problem solver for time-domain optical tomography with perfect parallel scaling

This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological tissue, but the high computational cost associated with its solution has hindered its use in time-domain optical-tomography and other areas. In this paper this problem is tackled by means of a number of computational and modeling innovations, including (1) A spatial parallel-decomposition strategy with perfect parallel scaling for the forward and inverse problems of optical tomography on parallel computer systems; and, (2) A Multiple Staggered Source method (MSS) that solves the inverse transport problem at a computational cost that is independent of the number of sources employed, and which significantly accelerates the reconstruction of the optical parameters: a six-fold MSS acceleration factor is demonstrated in this paper. Finally, this contribution presents (3) An intuitive derivation of the adjoint-based formulation for evaluation of functional gradients, including the highly-relevant general Fresnel boundary conditions—thus, in particular, generalizing results previously available for vacuum boundary conditions. Solutions of large and realistic 2D inverse problems are presented in this paper, which were produced on a 256-core computer system. The combined parallel/MSS acceleration approach reduced the required computing times by several orders of magnitude, from months to a few hours.