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
Journal PNAS nexus
Year 2026
DOI
10.1093/pnasnexus/pgag195
URL
https://doi.org/10.1093/pnasnexus/pgag195
Keywords Keywords not found

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