Efficient Deconvolution in Populational Inverse Problems
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Abstract (arXiv)
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing availability of data, but a major roadblock is blind deconvolution, arising when the observational noise distribution is unknown. However, when data originates from collections of physical systems, a population, it is possible to leverage this information to perform deconvolution. To this end, we propose a methodology leveraging large data sets of observations, collected from different instantiations of the same physical processes, to simultaneously deconvolve the data corrupting noise distribution, and to identify the distribution over model parameters defining the physical processes. A parameter-dependent mathematical model of the physical process is employed. A loss function characterizing the match between the observed data and the output of the mathematical model is defined; it is minimized as a function of the both the parameter inputs to the model of the physics and the parameterized observational noise. This coupled problem is addressed with a modified gradient descent algorithm that leverages specific structure in the noise model. Furthermore, a new active learning scheme is proposed, based on adaptive empirical measures, to train a surrogate model to be accurate in parameter regions of interest; this approach accelerates computation and enables automatic differentiation of black-box, potentially nondifferentiable, code computing parameter-to-solution maps. The proposed methodology is demonstrated on porous medium flow, damped elastodynamics, and simplified models of atmospheric dynamics.
Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 19 of its 92 references that are in the map. First posted on arXiv 26 May 2025.
Builds on
19 of 92 references.
References · 19
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 314
- 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 262
- 2020Model Reduction and Neural Networks for Parametric PDEscited by 258
- 2014Hilbert Space Methods for Reduced-Rank Gaussian Process Regressioncited by 88
- 2021POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decompositioncited by 79
- 2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
- 2017Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulationscited by 51
- 2020A probabilistic generative model for semi-supervised training of coarse-grained surrogates and enforcing physical constraints through virtual observablescited by 29
- 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
7 more
- 2020A greedy non-intrusive reduced order model for shallow water equationscited by 12
- 2024Efficient Prior Calibration From Indirect Datacited by 11
- 2024BiLO: Bilevel Local Operator Learning for PDE Inverse Problemscited by 8
- 2024Stochastic Inverse Problem: stability, regularization and Wasserstein gradient flowcited by 8
- 2016Hierarchical Bayesian Level Set Inversioncited by 6
- 2025Inverse Problems Over Probability Measure Spacecited by 6
- 2023Differential-Equation Constrained Optimization With Stochasticitycited by 4
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Citing papers per year: 2025: 2; 2026: 2.
4 papers.