Physics informed differentiable solvers for learning parametric solution manifolds in heterogeneous physical systems

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ID: 315441
2026
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Abstract
Abstract Quantifying parametric uncertainty in partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems. This challenge is relevant to a variety of fundamental and application-oriented implications where system properties exhibit significant (and often uncertain) spatial heterogeneity. We address this by reformulating a Physics-Informed Neural Network (PINN) as a differentiable solver that learns the continuous solution manifold for steady-state Darcy flow. Our framework requires only a single training run, circumventing the need for costly re-training for each new parameter instance. The approach is demonstrated through two representations of spatially heterogeneous hydraulic conductivity fields: a direct analytical form and a novel data-driven formulation resting on an autoencoder to create a low-dimensional latent encoding. A key innovation is the integration of the differentiable decoder into the physics-informed loss function, enabling on-the-fly reconstruction of complex conductivity fields. The approach yields accurate, mass-conserving flow solutions and supports efficient uncertainty quantification, providing a general methodology for physics-constrained data-driven modeling of heterogeneous systems.
Reference Key
openalex_W7162991833 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Milad Panahi, Giovanni Porta, Mònica Riva, Alberto Guadagnini
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Journal PNAS nexus
Year 2026
DOI
10.1093/pnasnexus/pgag195
URL
https://doi.org/10.1093/pnasnexus/pgag195
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