Reduced-order modeling for parameterized PDEs via implicit neural representations

• URL: http://arxiv.org/abs/2311.16410v1
• Date: Tue, 28 Nov 2023 01:35:06 GMT
• Title: Reduced-order modeling for parameterized PDEs via implicit neural representations
• Authors: Tianshu Wen, Kookjin Lee, Youngsoo Choi
• Abstract summary: We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) The proposed framework encodes PDE and utilizes a parametrized neural ODE (PNODE) to learn latent dynamics characterized by multiple PDE parameters. We evaluate the proposed method at a large Reynolds number and obtain up to speedup of O(103) and 1% relative error to the ground truth values.
• Score: 4.135710717238787
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR), which models physics signals in a continuous manner and independent of spatial/temporal discretization. The proposed framework encodes PDE and utilizes a parametrized neural ODE (PNODE) to learn latent dynamics characterized by multiple PDE parameters. PNODE can be inferred by a hypernetwork to reduce the potential difficulties in learning PNODE due to a complex multilayer perceptron (MLP). The framework uses an INR to decode the latent dynamics and reconstruct accurate PDE solutions. Further, a physics-informed loss is also introduced to correct the prediction of unseen parameter instances. Incorporating the physics-informed loss also enables the model to be fine-tuned in an unsupervised manner on unseen PDE parameters. A numerical experiment is performed on a two-dimensional Burgers equation with a large variation of PDE parameters. We evaluate the proposed method at a large Reynolds number and obtain up to speedup of O(10^3) and ~1% relative error to the ground truth values.

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