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Matthias Chung

Publications and source records attributed to Matthias Chung.

At least 19 recordsLinked to original sources
arXiv2026

Physics-conforming Latent Twins

Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

cs.LG↗
arXiv2026

Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification

Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but interpretable uncertainty. Providing fast inference alongside uncertainty estimates remains challenging yet desirable in numerous applications. We propose the Variational Sparse Paired Autoencoder (vsPAIR) to address this challenge. The architecture pairs a standard VAE encoding observations with a sparse VAE encoding quantities of interest (QoI), connected through a learned latent mapping. The variational structure enables uncertainty estimation, the paired architecture encourages interpretability by anchoring QoI representations to clean data, and sparse encodings provide structure by concentrating information into identifiable factors rather than diffusing across all dimensions. To validate the effectiveness of our proposed architecture, we conduct experiments on blind inpainting, computed tomography (CT), and initial-condition inference for the heat equation, demonstrating that vsPAIR is a capable inverse problem solver that can provide interpretable and structured uncertainty estimates.

cs.LG↗
arXiv2026

Latent Space Inference via Paired Autoencoders

This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and one for the observation space, connected by learned mappings between the autoencoders' latent spaces. These mappings enable a surrogate for regularized inversion and optimization in low-dimensional, informative latent spaces. Our flexible framework can work with partial, noisy, or out-of-distribution data, all while maintaining consistency with the underlying physical models. The paired autoencoders enable reconstruction of corrupted data, and then use the reconstructed data for parameter estimation, which produces more accurate reconstructions compared to paired autoencoders alone and end-to-end encoder-decoders of the same architecture, especially in scenarios with data inconsistencies. We demonstrate our approaches on two imaging examples in medical tomography and geophysical seismic-waveform inversion, but the described approaches are broadly applicable to a variety of inverse problems in scientific and engineering applications.

cs.LG↗
arXiv2025

Latent Twins: A Framework for Scene Recognition and Fast Radiative Transfer Inversion in FORUM All-Sky Observations

The FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) mission will provide, for the first time, systematic far-infrared spectral measurements of Earth's outgoing radiation, enabling improved understanding of atmospheric processes and the radiation budget. Retrieving atmospheric states from these observations constitutes a high-dimensional, ill-posed inverse problem, particularly under cloudy-sky conditions where multiple-scattering effects are present. In this work, we develop a data-driven, physics-aware inversion framework for FORUM all-sky retrievals based on latent twins: coupled autoencoders for atmospheric states and spectra, combined with bidirectional latent-space mappings. A lightweight model-consistency correction ensures physically plausible cloud variable reconstructions. The resulting framework demonstrates potential for retrievals of atmospheric, cloud and surface variables, providing information that can serve as a prior, initial guess, or surrogate for computationally expensive full-physics inversion methods. It also enables robust scene classification and near-instantaneous inference, making it suitable for operational near-real-time applications. We demonstrate its performance on synthetic FORUM-like data and discuss implications for future data assimilation and climate studies.

physics.ao-ph↗
arXiv2025

Neural Optimal Design of Experiment for Inverse Problems

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.

cs.LG↗
arXiv2025

Variable Projected Augmented Lagrangian Methods for Generalized Lasso Problems

We introduce variable projected augmented Lagrangian (VPAL) methods for solving generalized nonlinear Lasso problems with improved speed and accuracy. By eliminating the nonsmooth variable via soft-thresholding, VPAL transforms the problem into a smooth reduced formulation. For linear models, we develop a preconditioned variant that mimics Newton-type updates and yields significant acceleration. We prove convergence guarantees for both standard and preconditioned VPAL under mild assumptions and show that variable projection leads to sharper convergence and higher solution quality. The method seamlessly extends to nonlinear inverse problems, where it outperforms traditional approaches in applications such as phase retrieval and contrast enhanced MRI (LIP-CAR). Across tasks including deblurring, inpainting, and sparse-view tomography, VPAL consistently delivers state-of-the-art reconstructions, positioning variable projection as a powerful tool for modern large-scale inverse problems.

math.OC↗
arXiv2025

Latent Twins

Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical PDEs, dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With \emph{Latent Twins}, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ODEs and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with DeepONet and forecasts with a 4D-Var baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.

cs.LG↗
arXiv2025

Optimal Linear Baseline Models for Scientific Machine Learning

Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they remain theoretically opaque, which hinders adoption in contexts where interpretability is paramount. In contrast, linear neural networks serve as a simple yet effective foundation for gaining insight into these complex relationships. In this work, we develop a unified theoretical framework for analyzing linear encoder-decoder architectures through the lens of Bayes risk minimization for solving data-driven scientific machine learning problems. We derive closed-form, rank-constrained linear and affine linear optimal mappings for forward modeling and inverse recovery tasks. Our results generalize existing formulations by accommodating rank-deficiencies in data, forward operators, and measurement processes. We validate our theoretical results by conducting numerical experiments on datasets from simple biomedical imaging, financial factor analysis, and simulations involving nonlinear fluid dynamics via the shallow water equations. This work provides a robust baseline for understanding and benchmarking learned neural network models for scientific machine learning problems.

cs.LG↗
arXiv2025

Good Things Come in Pairs: Paired Autoencoders for Inverse Problems

In this book chapter, we discuss recent advances in data-driven approaches for inverse problems. In particular, we focus on the \emph{paired autoencoder} framework, which has proven to be a powerful tool for solving inverse problems in scientific computing. The paired autoencoder framework is a novel approach that leverages the strengths of both data-driven and model-based methods by projecting both the data and the quantity of interest into a latent space and mapping these latent spaces to provide surrogate forward and inverse mappings. We illustrate the advantages of this approach through numerical experiments, including seismic imaging and classical inpainting: nonlinear and linear inverse problems, respectively. Although the paired autoencoder framework is likelihood-free, it generates multiple data- and model-based reconstruction metrics that help assess whether examples are in or out of distribution. In addition to direct model estimates from data, the paired autoencoder enables latent-space refinement to fit the observed data accurately. Numerical experiments show that this procedure, combined with the latent-space initial guess, is essential for high-quality estimates, even when data noise exceeds the training regime. We also introduce two novel variants that combine variational and paired autoencoder ideas, maintaining the original benefits while enabling sampling for uncertainty analysis.

cs.LG↗
arXiv2025

VPAL: A novel method to reduce reconstruction time for 5D free-running imaging

Purpose: Ferumoxytal-enhanced 5D free-running whole heart CMR provides image quality comparable to CTA, but requires hours-long reconstruction time, preventing clinical usage. This study developed a variable projection augmented Lagrangian (VPAL) method for 5D motion-resolved image reconstruction and compared it with alternating direction method of multipliers (ADMM) in five numerical simulations and 15 in-vivo pediatric data set. Approach: Relative error of the reconstructed images against the ground-truth images was assessed in numerical simulations. In-vivo analysis compared reconstruction time, mid-short axis (SA) blood-myocardium sharpness, left ventricular ejection fraction (LVEF), and a radiologist's image quality ratings between VPAL and ADMM. A paired t-test (p<0.05) was used to determine statistical significance, while linear regression and Bland-Altman analysis for agreement assessments. Results: VPAL and ADMM had similar relative errors compared to the ground truth, p = 0.07. In in-vivo datasets, VPAL reduced the reconstruction time from 16.3 +/- 3.6 hours (ADMM) to 4.7 +/- 1.1 hours (VPAL), p=1e-10. Blood-myocardium border sharpness in VPAL closely correlates to ADMM , R^2 = 0.97. The LVEFs values measured by VPAL and ADMM reconstructions are largely similar, 56 +/- 6 % in ADMM and 56 +/- 6 % in VPAL, p=0.55. Both VPAL and ADMM reconstructions have good to excellent diagnostic ratings (VPAL vs. ADMM: 3.9 +/- 0.3 vs. 3.8 +/- 0.4 in 2-chamber; 3.9 +/- 0.4 vs. 3.9 +/- in 4-chamber; 3.7 +/- 0.5 vs. 3.7 +/- 0.5 in mid-SA reformatted views. Conclusion: VPAL enables faster reconstruction than ADMM while maintaining equivalent image quality for functional assessments, supporting its potential for clinical use.

physics.med-ph↗
arXiv2025

Fast $\ell_1$-Regularized EEG Source Localization Using Variable Projection

Electroencephalograms (EEG) are invaluable for treating neurological disorders, however, mapping EEG electrode readings to brain activity requires solving a challenging inverse problem. Due to the time series data, the use of $\ell_1$ regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of $\ell_1$ regularization, $\ell_2$-based approaches such as sLORETA are used in practice. In this work, we formulate EEG source localization as a graphical generalized elastic net inverse problem and present a variable projected algorithm (VPAL) suitable for fast EEG source localization. We prove convergence of this solver for a broad class of separable convex, potentially non-smooth functions subject to linear constraints and include a modification of VPAL that reconstructs time points in sequence, suitable for real-time reconstruction. Our proposed methods are compared to state-of-the-art approaches including sLORETA and other methods for $\ell_1$-regularized inverse problems.

stat.ML↗
arXiv2025

A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization

In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are used to efficiently represent the input and target spaces separately and optimal mappings are learned between latent spaces, thus enabling forward and inverse surrogate mappings. We focus on interpretations using Bayes risk and empirical Bayes risk minimization, and we provide various theoretical results and connections to existing works on low-rank matrix approximations. Similar to end-to-end approaches, our paired approach creates a surrogate model for forward propagation and regularized inversion. However, our approach outperforms existing approaches in scenarios where training data for unsupervised learning are readily available but training pairs for supervised learning are scarce. Furthermore, we show that cheaply computable evaluation metrics are available through this framework and can be used to predict whether the solution for a new sample should be predicted well.

cs.LG↗
arXiv2024

Paired Wasserstein Autoencoders for Conditional Sampling

Generative autoencoders learn compact latent representations of data distributions through jointly optimized encoder--decoder pairs. In particular, Wasserstein autoencoders (WAEs) minimize a relaxed optimal transport (OT) objective, where similarity between distributions is measured through a cost-minimizing joint distribution (OT coupling). Beyond distribution matching, neural OT methods aim to learn mappings between two data distributions induced by an OT coupling. Building on the formulation of the WAE loss, we derive a novel loss that enables sampling from OT-type couplings via two paired WAEs with shared latent space. The resulting fully parametrized joint distribution yields (i) learned cost-optimal transport maps between the two data distributions via deterministic encoders. Under cost-consistency constraints, it further enables (ii) conditional sampling from an OT-type coupling through stochastic decoders. As a proof of concept, we use synthetic data with known and visualizable marginal and conditional distributions.

cs.LG↗
arXiv2024

A physics-aware data-driven surrogate approach for fast atmospheric radiative transfer inversion

FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) was selected in 2019 as the ninth Earth Explorer mission by the European Space Agency (ESA). Its primary objective is to collect interferometric measurements in the Far-InfraRed (FIR) spectral range, which accounts for 50\% of Earth's outgoing longwave radiation emitted into space, and will be observed from space for the first time. Accurate measurements of the FIR at the top of the atmosphere are crucial for improving climate models. Current instruments are insufficient, necessitating the development of advanced computational techniques. To ensure the quality of the mission data, an End-to-End Simulator (E2ES) was developed to simulate the measurement process and evaluate the effects of instrument characteristics and environmental factors. The core challenge of the mission is solving the retrieval problem, which involves estimating atmospheric properties from the radiance spectra observed by the satellite. This problem is ill-posed and regularization techniques are necessary. In this work, we present a novel and fast data-driven approach to approximate the inverse mapping. In the first phase, we generate an initial approximation of the inverse mapping using only simulated FORUM data. In the second phase, we improve this approximation by introducing climatological data as a priori information and using a neural network to estimate the optimal regularization parameters. While our approach does not match the precision of full-physics retrieval methods, its key advantage is the ability to deliver results almost instantaneously, making it highly suitable for real-time applications. Furthermore, the proposed method can provide more accurate a priori estimates for full-physics methods, thereby improving the overall accuracy of the retrieved atmospheric profiles.

physics.ao-ph↗
arXiv2024

Sparse $L^1$-Autoencoders for Scientific Data Compression

Scientific datasets present unique challenges for machine learning-driven compression methods, including more stringent requirements on accuracy and mitigation of potential invalidating artifacts. Drawing on results from compressed sensing and rate-distortion theory, we introduce effective data compression methods by developing autoencoders using high dimensional latent spaces that are $L^1$-regularized to obtain sparse low dimensional representations. We show how these information-rich latent spaces can be used to mitigate blurring and other artifacts to obtain highly effective data compression methods for scientific data. We demonstrate our methods for short angle scattering (SAS) datasets showing they can achieve compression ratios around two orders of magnitude and in some cases better. Our compression methods show promise for use in addressing current bottlenecks in transmission, storage, and analysis in high-performance distributed computing environments. This is central to processing the large volume of SAS data being generated at shared experimental facilities around the world to support scientific investigations. Our approaches provide general ways for obtaining specialized compression methods for targeted scientific datasets.

cs.LG↗
arXiv2024

Paired Autoencoders for Likelihood-free Estimation in Inverse Problems

We consider the solution of nonlinear inverse problems where the forward problem is a discretization of a partial differential equation. Such problems are notoriously difficult to solve in practice and require minimizing a combination of a data-fit term and a regularization term. The main computational bottleneck of typical algorithms is the direct estimation of the data misfit. Therefore, likelihood-free approaches have become appealing alternatives. Nonetheless, difficulties in generalization and limitations in accuracy have hindered their broader utility and applicability. In this work, we use a paired autoencoder framework as a likelihood-free estimator for inverse problems. We show that the use of such an architecture allows us to construct a solution efficiently and to overcome some known open problems when using likelihood-free estimators. In particular, our framework can assess the quality of the solution and improve on it if needed. We demonstrate the viability of our approach using examples from full waveform inversion and inverse electromagnetic imaging.

cs.LG↗
arXiv2023

Image reconstructions using sparse dictionary representations and implicit, non-negative mappings

Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as smoothness, into the solution can overcome these challenges. In this work, we encode prior knowledge using a non-negative patch dictionary, which effectively learns a basis from a training set of natural images. In this dictionary basis, we desire solutions that are non-negative and sparse (i.e., contain many zero entries). With these constraints, standard methods for solving discrete linear inverse problems are not directly applicable. One such approach is the modified residual norm steepest descent (MRNSD), which produces non-negative solutions but does not induce sparsity. In this paper, we provide two methods based on MRNSD that promote sparsity. In our first method, we add an $\ell_1$-regularization term with a new, optimal step size. In our second method, we propose a new non-negative, sparsity-promoting mapping of the solution. We compare the performance of our proposed methods on a number of numerical experiments, including deblurring, image completion, computer tomography, and superresolution. Our results show that these methods effectively solve discrete linear inverse problems with non-negativity and sparsity constraints.

math.NA↗
arXiv2023

Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks

In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary to standard inverse problems, these approaches are \emph{goal-oriented} in that the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. This may be particularly challenging, especially for nonlinear, possibly unknown, operators and nonstandard prior assumptions. We harness recent advances in machine learning, i.e., VED networks, to describe a data-driven approach to large-scale inverse problems. This enables a real-time goal-oriented uncertainty quantification for the QoI. One of the advantages of our approach is that we avoid the need to solve challenging inversion problems by training a network to approximate the mapping from observations to QoI. Another main benefit is that we enable uncertainty quantification for the QoI by leveraging probability distributions in the latent space. This allows us to efficiently generate QoI samples and circumvent complicated or even unknown forward models and prediction operators. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of the approach.

math.NA↗