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arXiv Machine Learning By Zhikun Zhang, Guanyu Pan, Xiangjun Wang, Yong Xu, Guangtao Zhang

Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models

Read the original on arXiv Machine Learning →

The paper introduces a two‑stage physics‑informed deep learning framework for solving inverse problems in partial differential equations with jump discontinuities in coefficients. The first stage uses a dual‑network architecture to approximate the PDE solution and a relaxed continuous surrogate of the coefficient field, followed by Bayesian inference with Gaussian mixture and birth‑death Markov chain models to estimate coefficient regimes and transition regions. The second stage reformulates the inverse problem as a constrained estimator with a hard piecewise‑constant coefficient representation, achieving accurate parameter estimation with acceptable computational costs across various PDE types.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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