Data-driven Reconstruction Research Articles

Physics-informed data-driven reconstruction of turbulent wall-bounded flows from planar measurements

Obtaining accurate and dense three-dimensional estimates of turbulent wall-bounded flows is notoriously challenging, and this limitation negatively impacts geophysical and engineering applications, such as weather forecasting, climate predictions, air quality monitoring, and flow control. This study introduces a physics-informed variational autoencoder model that reconstructs realizable three-dimensional turbulent velocity fields from two-dimensional planar measurements thereof. Physics knowledge is introduced as soft and hard constraints in the loss term and network architecture, respectively, to enhance model robustness and leverage inductive biases alongside observational ones. The performance of the proposed framework is examined in a turbulent open-channel flow application at friction Reynolds number Reτ=250. The model excels in precisely reconstructing the dynamic flow patterns at any given time and location, including turbulent coherent structures, while also providing accurate time- and spatially-averaged flow statistics. The model outperforms state-of-the-art classical approaches for flow reconstruction such as the linear stochastic estimation method. Physical constraints provide a modest but discernible improvement in the prediction of small-scale flow structures and maintain better consistency with the fundamental equations governing the system when compared to a purely data-driven approach.

Spectral reconstruction using neural networks in filter-array-based chip-size spectrometers

Abstract Spectral reconstruction in filter-based miniature spectrometers remains challenging due to the ill-posed nature of identifying stable solutions. Even minor deviations in sensor data can cause misleading reconstruction outcomes, particularly in the absence of proper regularization techniques. While previous research has attempted to mitigate this instability by incorporating neural networks into the reconstruction pipeline to denoise the data before reconstruction or correct it after reconstruction, these approaches have not fully resolved the underlying issue. This work functions as a proof-of-concept for data-driven reconstruction that relies exclusively on neural networks, thereby circumventing the need to address the ill-posed inverse problem. We curate a dataset holding transmission spectra from various colored foils, commonly used in theatrical, and train five distinct neural networks optimized for spectral reconstruction. Subsequently, we benchmark these networks against each other and compare their reconstruction capabilities with a linear reconstruction model to show the applicability of cognitive sensors to the problem of spectral reconstruction. In our testing, we discovered that (i) spectral reconstruction can be achieved using neural networks with an end-to-end approach, and (ii) while a classic linear model can perform equal to neural networks under optimal conditions, the latter can be considered more robust against data deviations.

Prediction of spatiotemporal dynamic systems by data-driven reconstruction

Prediction in nonlinear systems is critical and challenging in various fields. Data-driven methods provide the theoretical basis for predicting nonlinear systems. On this basis, a data-driven prediction framework for improved reservoir computing (RC) combined with higher order dynamic mode decomposition (HODMD) is proposed. First, HODMD extracts the eigenmodes of the nonlinear system through higher order Koopman assumptions and retains the principal modes to reconstruct the system. The subsequent process uses the reconstructed system to train a unique weight matrix through the quadratic readout of the reservoir feature vectors; the reusable feature of RC training is employed to accomplish autonomous prediction of the nonlinear system. The practical consideration of the data-driven prediction framework is to enhance the ability of the RC to learn the internal evolutionary laws of the nonlinear system. Numerical results by Kuramoto-Sivashinsky equation demonstrate that the HODMD-RC framework improves the short-term and long-term prediction of nonlinear systems.

Data-driven reconstruction of chaotic dynamical equations: The Hénon–Heiles type system

In this study, the classical two-dimensional potential VN=12mω2r2+1NrNsin(Nθ), N∈Z+, is considered. At N=1,2, the system is superintegrable and integrable, respectively, whereas for N>2 it exhibits a richer chaotic dynamics. For instance, at N=3 it coincides with the Hénon–Heiles system. The periodic, quasi-periodic and chaotic motions are systematically characterized employing time series, Poincaré sections, symmetry lines and the largest Lyapunov exponent as a function of the energy E and the parameter N. Concrete results for the lowest cases N=3,4 are presented in complete detail. This model is used as a benchmark system to estimate the accuracy of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method, a data-driven algorithm which reconstructs the underlying governing dynamical equations. We pay special attention at the transition from regular motion to chaos and how this influences the precision of the algorithm. In particular, it is shown that SINDy is a robust and stable tool possessing the ability to generate non-trivial approximate analytical expressions for periodic trajectories as well.

A model-independent precision test of general relativity using bright standard sirens from ongoing and upcoming detectors

Abstract Gravitational waves (GWs) provide a new avenue to test Einstein’s General Relativity (GR) using the ongoing and upcoming GW detectors by measuring the redshift evolution of the effective Planck mass proposed by several modified theories of gravity. We propose a model-independent, data-driven approach to measure any deviation from GR in the GW propagation effect by combining multi-messenger observations of GW sources accompanied by EM counterparts, commonly known as bright sirens (Binary Neutron Star (BNS) and Neutron Star Black Hole systems (NSBH)). We show that by combining the GW luminosity distance measurements from bright sirens with the Baryon Acoustic Oscillation (BAO) measurements derived from galaxy clustering, and the sound horizon measurements from the Cosmic Microwave Background (CMB), we can make a data-driven reconstruction of deviation of the variation of the effective Planck mass (jointly with the Hubble constant) as a function of cosmic redshift. Using this technique, we achieve a precise measurement of GR with redshift (z) with a precision of approximately 7.9 % for BNSs at redshift z=0.075 and 10 % for NSBHs at redshift z=0.225 with 5 years of observation from LIGO-Virgo-KAGRA network of detectors. Employing Cosmic Explorer and Einstein Telescope for just 1 year yields the best precision of about 1.62 % for BNSs and 2 % for NSBHs at redshift z=0.5 on the evolution of the frictional term, and a similar precision up to z=1. This measurement can discover potential deviation from any kind of model that impacts GW propagation with ongoing and upcoming observations.

Revealing Higher-Order Interactions in High-Dimensional Complex Systems: A Data-Driven Approach

Natural and manmade complex systems are comprised of different elementary units, being either system components or diverse subsystems as in the case of networked systems. These units interact with each other in a possibly nonlinear way, which results in a complex dynamics that is generally dissipative and nonstationary. One of the challenges in the modeling of such systems is the identification of not only pairwise but, more importantly, higher-order interactions, together with their directions and strengths from measured multivariate time series. Here, we propose a novel data-driven approach for characterizing interactions of different orders. Our approach is based on solving a set of linear equations constructed from Kramers-Moyal coefficients derived from statistical moments of N-dimensional multivariate time series. We demonstrate the substantial potential for applications by a data-driven reconstruction of interactions in various multidimensional and networked dynamical systems. Published by the American Physical Society 2024

Invertible residual networks in the context of regularization theory for linear inverse problems

Abstract Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step procedure. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings.

Improving brain tumor segmentation with anatomical prior-informed pre-training.

Precise delineation of glioblastoma in multi-parameter magnetic resonance images is pivotal for neurosurgery and subsequent treatment monitoring. Transformer models have shown promise in brain tumor segmentation, but their efficacy heavily depends on a substantial amount of annotated data. To address the scarcity of annotated data and improve model robustness, self-supervised learning methods using masked autoencoders have been devised. Nevertheless, these methods have not incorporated the anatomical priors of brain structures. This study proposed an anatomical prior-informed masking strategy to enhance the pre-training of masked autoencoders, which combines data-driven reconstruction with anatomical knowledge. We investigate the likelihood of tumor presence in various brain structures, and this information is then utilized to guide the masking procedure. Compared with random masking, our method enables the pre-training to concentrate on regions that are more pertinent to downstream segmentation. Experiments conducted on the BraTS21 dataset demonstrate that our proposed method surpasses the performance of state-of-the-art self-supervised learning techniques. It enhances brain tumor segmentation in terms of both accuracy and data efficiency. Tailored mechanisms designed to extract valuable information from extensive data could enhance computational efficiency and performance, resulting in increased precision. It's still promising to integrate anatomical priors and vision approaches.

Machine learning methods for nonlinear dimensionality reduction of the thermospheric density field

Accurate prediction of the thermospheric density field has recently been gaining a lot of attention, due to an outstanding increase in space operations in Low-Earth Orbit, in the context of the NewSpace. In order to model such high-dimensional, non-Gaussian systems, Reduced-Order Models (ROMs) have been developed against existing physics-based density models. In general, the data-driven reconstruction of dynamical systems usually consists of two steps of compression and prediction. In this paper, we focus on the compression step and assess state-of-the-art order reduction methodologies such as autoencoders, linear, and nonlinear Principal Component Analysis (PCA). We show that Kernel-based PCA, a nonlinear generalization of PCA, can perform better than Neural Networks in representing the model in low-dimensional space in terms of accuracy, computational time, and energy consumption for both the Lorenz system, a chaotic dynamical system developed in the context of atmospheric modeling, and the thermospheric density.

Data-driven reconstruction of stochastic dynamical equations based on statistical moments

Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid. If such processes are Markov, then their probability distribution is governed by the Kramers–Moyal (KM) equation, a partial differential equation that involves an infinite number of coefficients, which depend on the state variable. The KM coefficients must be evaluated based on measured time series for a data-driven reconstruction of the governing equations for the stochastic dynamics. We present an accurate method of computing the KM coefficients, which relies on computing the coefficients’ conditional moments based on the statistical moments of the time series. The method’s advantages over state-of-the-art approaches are demonstrated by investigating prototypical one-dimensional stochastic processes with well-known properties.

Data-driven reconstruction of partially observed dynamical systems

Abstract. The state of the atmosphere, or of the ocean, cannot be exhaustively observed. Crucial parts might remain out of reach of proper monitoring. Also, defining the exact set of equations driving the atmosphere and ocean is virtually impossible because of their complexity. The goal of this paper is to obtain predictions of a partially observed dynamical system without knowing the model equations. In this data-driven context, the article focuses on the Lorenz-63 system, where only the second and third components are observed and access to the equations is not allowed. To account for those strong constraints, a combination of machine learning and data assimilation techniques is proposed. The key aspects are the following: the introduction of latent variables, a linear approximation of the dynamics and a database that is updated iteratively, maximizing the likelihood. We find that the latent variables inferred by the procedure are related to the successive derivatives of the observed components of the dynamical system. The method is also able to reconstruct accurately the local dynamics of the partially observed system. Overall, the proposed methodology is simple, is easy to code and gives promising results, even in the case of small numbers of observations.

Data-Driven Reconstruction of Dynamical Forces and Responses through Bayesian Expectation-Maximization and Modal Reduction Methods

This paper presents a new Bayesian approach for estimating input and state in linear structures using response-only measurements. The proposed approach benefits from a modally reduced state-space model, which circumvents the dimensionality of dynamical responses in complex structures through a low-dimensional subspace. It also substitutes unknown physical forces with a set of equivalent modal forces, which is beneficial when the magnitude and location of input forces are unknown. In this work, these forces are characterized through the conventional random walk model and a class of stationary Gaussian processes. Subsequently, an augmented state-space model is constructed to describe modal states and input loads. Based on this model, a Bayesian expectation-maximization (BEM) methodology is developed to identify the input, state, and noise parameters. This noise identification perspective activates uncertainty quantification in joint input-state estimation problems and enables quantifying the degree of confidence in the estimated quantities. When the proposed method is tested using numerical and experimental examples, accurate estimations and reasonable uncertainty bounds are acquired for the dynamical state and input forces. Although the literature reports the superiority of the Gaussian process latent force model over the random walk model without using a unified noise calibration strategy, this study, to our best knowledge, is the first effort to compare and interpret the results on a consistent basis where the noise and input characteristics are all identified from the data through BEM.

OpenSpyrit: an ecosystem for open single-pixel hyperspectral imaging.

This paper describes OpenSpyrit, an open access and open source ecosystem for reproducible research in hyperspectral single-pixel imaging, composed of SPAS (a Python single-pixel acquisition software), SPYRIT (a Python single-pixel reconstruction toolkit) and SPIHIM (a single-pixel hyperspectral image collection). The proposed OpenSpyrit ecosystem responds to the need for reproducibility and benchmarking in single-pixel imaging by providing open data and open software. The SPIHIM collection, which is the first open-access FAIR dataset for hyperspectral single-pixel imaging, currently includes 140 raw measurements acquired using SPAS and the corresponding hypercubes reconstructed using SPYRIT. The hypercubes are reconstructed by both inverse Hadamard transformation of the raw data and using the denoised completion network (DC-Net), a data-driven reconstruction algorithm. The hypercubes obtained by inverse Hadamard transformation have a native size of 64 × 64 × 2048 for a spectral resolution of 2.3 nm and a spatial resolution that is comprised between 182.4 µm and 15.2 µm depending on the digital zoom. The hypercubes obtained using the DC-Net are reconstructed at an increased resolution of 128 × 128 × 2048. The OpenSpyrit ecosystem should constitute a reference to support benchmarking for future developments in single-pixel imaging.

Learning torus PCA-based classification for multiscale RNA correction with application to SARS-CoV-2

Abstract Three-dimensional RNA structures frequently contain atomic clashes. Usually, corrections approximate the biophysical chemistry, which is computationally intensive and often does not correct all clashes. We propose fast, data-driven reconstructions from clash-free benchmark data with two-scale shape analysis: microscopic (suites) dihedral backbone angles, mesoscopic sugar ring centre landmarks. Our analysis relates concentrated mesoscopic scale neighbourhoods to microscopic scale clusters, correcting within-suite-backbone-to-backbone clashes exploiting angular shape and size-and-shape Fréchet means. Validation shows that learned classes highly correspond with literature clusters and reconstructions are well within physical resolution. We illustrate the power of our method using cutting-edge SARS-CoV-2 RNA.

Rapid response data-driven reconstructions for storm surge around New Zealand

In conjunction with tides, storm surge is one major driver of coastal flooding associated with storm events. Because local inundation is strongly modulated by the local shape of the coastline and the bathymetric slope, accurate storm surge predictions using traditional numerical models require the use of very fine grids and are hence resource intensive. Therefore, the performance of a live prediction system based on such methods will likely be subject to a trade-off between prediction accuracy, prediction speed and cost.This study explores the use of data driven methods as an alternative to numerical models to reconstruct the daily storm surge maximum levels along the entire coast of New Zealand. Firstly, several atmospheric predictors are utilized that incorporate different variables, time lags and spatial domains, using 3 statistical models, in a selected number of locations in New Zealand, to find the combination that optimizes the reconstruction. Finally, the storm surge daily maxima are reconstructed with the different statistical models along the entire coast, using the best performing predictor.Results show very good performance for the best atmospheric predictor and statistical model, providing average values of 0.88 for the Pearson correlation coefficient and 4.3 cm for the root mean squared error metric (RMSE) (the average value for the RMSE in the 99% percentile is 8.2 cm). For the Kling–Gupta Efficiency (KGE; incorporating 3 sub-metrics: correlation, bias term and variability term), which is the metric used to rank the models, the average value is 0.82.Our results highlight the suitability of data driven models to simulate storm surge maximum levels, and prove the methodology is appropriate for finding a well performing atmospheric predictor that is able for reconstruct these values. Moreover, this methodology can be also applied to new variables, regions and problems, as there are no physical restrictions on the used predictors nor predictands.

Imaging based on Compton scattering: model uncertainty and data-driven reconstruction methods

The recent development of scintillation crystals combined with γ-rays sources opens the way to an imaging concept based on Compton scattering, namely Compton scattering tomography. The associated inverse problem rises many challenges: non-linearity, multiple order-scattering and high level of noise. Already studied in the literature, these challenges lead unavoidably to uncertainty of the forward model. This work proposes to study exact and approximated forward models and develops two data-driven reconstruction algorithms able to tackle the inexactness of the forward model. The first one is based on the projective method called regularized sequential subspace optimization (RESESOP). We consider here a finite dimensional restriction of the semi-discrete forward model and show its well-posedness and regularization properties. The second one considers the unsupervised learning method, deep image prior, inspired by the construction of the model uncertainty in RESESOP. The methods are validated on Monte-Carlo data.

Data-driven reconstruction of rough surfaces from acoustic scattering

This work investigates the use of data-driven approaches for reconstructing rough surfaces from scattered sound. The proposed methods stand as alternatives to matrix inversion, which requires a linearisation of the dependence on the surface parameters. Here, a large dataset was formed from different surface realisations alongside the corresponding scattered acoustic field, estimated through the Kirchhoff Approximation. Limiting this work to the reconstruction of a static surface, K-Nearest Neighbours, Random Forests, and a stochastic approach are compared to recover a parameterisation of surfaces using the scattered acoustical pressure as input. The models are then validated against a laboratory experiment alongside methods highlighted in Dolcetti et. al., JSV, 2021. The models are tested at a frequency that best fits the lab uncertainties, then tested on a broad frequency range. This scheme provides relatively accurate results in comparison to the approaches tested. Estimation errors as well as robustness in the presence of noise are discussed.

The last Fennoscandian Ice Sheet glaciation on the Kola Peninsula and Russian Lapland (Part 1): Ice flow configuration

A detailed reconstruction of palaeo-ice flow configuration is lacking for the Kola Peninsula and Russian Lapland, northwest Arctic Russia. This study presents, for the first time, a 14-stage reconstruction of the last Fennoscandian Ice Sheet (FIS) flow configuration on the Kola Peninsula and Russian Lapland from build-up to complete deglaciation. Flowsets (n = 102) and cross-cutting bedform assemblages identified from a high-resolution subglacial bedform record (subglacial lineations and subglacial ribs) are combined with subglacially streamlined bedrock data to define ice flow patterns, ice divides, ice margins, and glaciation styles of the last glaciation through relative time.The results demonstrate that the FIS flow configuration was not static. The FIS advanced eastwards across the region from Scandinavia, rather than expanding from local upland areas, and established a predominantly cold-based ice mass on the Kola Peninsula with an extensive adjacent warm-based ice lobe in the White Sea. An east-west aligned ice divide was located on the Kola Peninsula and Russian Lapland during the ice sheet build-up stages. However, this divide was short-lived as the White Sea lobe dominated ice flow on the peninsula during the local-Last Glacial Maximum, and ice predominantly flowed across the region from the main ice dispersal zone that was centred over the Gulf of Bothnia during deglaciation. Deglaciation on the peninsula was initially characterised by cold-based ice sheet retreat on the central eastern Kola Peninsula and warm-based ice lobe retreat in the White Sea. Continued deglaciation was characterised by ice sheet thinning, exposing mountain summits as nunataks behind the ice sheet margin, with topography constraining ice flow around upland areas. Ice streams in the region were drivers and consequences of continued ice sheet configuration change throughout glaciation. Four palaeo ice streams – (i) the Imandra Ice Stream; (ii) the Lovozero Ice Stream; (iii) the Kanozero Ice Stream; and (iv) the Kuusamo Ice Stream – and three possible palaeo-ice stream pathways are identified.We consider our ice flow configuration reconstruction to be the simplest palaeo-glaciological interpretation of the bedform record of the Kola Peninsula and Russian Lapland. The empirically-based reconstruction of ice flow geometry provides a regional framework and context for interpreting results from local-scale fieldwork, and is presented in a format that can be utilised by numerical ice sheet modellers to test and verify their models. The results underpin a new data-driven reconstruction of the last FIS in northwest Arctic Russia that we present in Part 2 of this study.

Connecting Solar Orbiter remote-sensing observations and Parker Solar Probe in situ measurements with a numerical MHD reconstruction of the Parker spiral

As a key feature, NASA’s Parker Solar Probe (PSP) and ESA-NASA’s Solar Orbiter (SO) missions cooperate to trace solar wind and transients from their sources on the Sun to the inner interplanetary space. The goal of this work is to accurately reconstruct the interplanetary Parker spiral and the connection between coronal features observed remotely by the Metis coronagraph on-board SO and those detected in situ by PSP at the time of the first PSP-SO quadrature of January 2021. We use the Reverse in situ and MHD Approach (RIMAP), a hybrid analytical-numerical method performing data-driven reconstructions of the Parker spiral. RIMAP solves the MHD equations on the equatorial plane with the PLUTO code, using the measurements collected by PSP between 0.1 and 0.2 AU as boundary conditions. Our reconstruction connects density and wind speed measurements provided by Metis (3–6 solar radii) to those acquired by PSP (21.5 solar radii) along a single streamline. The capability of our MHD model to connect the inner corona observed by Metis and the super Alfvénic wind measured by PSP, not only confirms the research pathways provided by multi-spacecraft observations, but also the validity and accuracy of RIMAP reconstructions as a possible test bench to verify models of transient phenomena propagating across the heliosphere, such as coronal mass ejections, solar energetic particles and solar wind switchbacks.

Data-Driven Reconstruction of Spectral Conductivity and Chemical Potential Using Thermoelectric Transport Properties

The spectral conductivity, i.e., the electrical conductivity as a function of the Fermi energy, is a cornerstone in determining the thermoelectric transport properties of electrons. However, the spectral conductivity depends on sample-specific properties such as carrier concentrations, vacancies, charge impurities, chemical compositions, and material microstructures, making it difficult to relate the experimental result with the theoretical prediction directly. Here, we propose a data-driven approach based on machine learning to reconstruct the spectral conductivity and chemical potential from the thermoelectric transport data. Using this machine learning method, we first demonstrate that the spectral conductivity and temperature-dependent chemical potentials can be recovered within a simple toy model. In a second step, we apply our method to experimental data in doped one-dimensional telluride Ta$_4$SiTe$_4$~[T. Inohara, \textit{et al.}, Appl. Phys. Lett. \textbf{110}, 183901 (2017)] to reconstruct the spectral conductivity and chemical potential for each sample. Furthermore, the thermal conductivity of electrons and the maximal figure of merit $ZT$ are estimated from the reconstructed spectral conductivity, which provides accurate estimates beyond the Wiedemann-Franz law. Our study clarifies the connection between the thermoelectric transport properties and the low-energy electronic states of real materials, and establishes a promising route to incorporate experimental data into traditional theory-driven workflows.