Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

Roy, Sumanta; Sarkar, Dibakar Roy; Annavarapu, Chandrasekhar; Roy, Pratanu; Lecampion, Brice; Valiveti, Dakshina Murthy

doi:10.1016/j.finel.2024.104305

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

Journal Article · Fri Jan 10 00:00:00 EST 2025 · Finite Elements in Analysis and Design

DOI:https://doi.org/10.1016/j.finel.2024.104305· OSTI ID:2560970

Roy, Sumanta ^[1]; Sarkar, Dibakar Roy ^[1]; ^[1]; Roy, Pratanu ^[2]; Lecampion, Brice ^[3]; Valiveti, Dakshina Murthy ^[4]

Indian Institute of Technology Madras, Chennai (India)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland)
ExxonMobil Technology and Engineering, Spring, TX (United States)

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2560970

Report Number(s):: LLNL--JRNL-868961; 1105382

Journal Information:: Finite Elements in Analysis and Design, Journal Name: Finite Elements in Analysis and Design Vol. 244; ISSN 0168-874X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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