Year: 2024
Type: preprint
Abstract: This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for modeling latent dynamics over time with a decoder that reconstructs PDE solutions from the corresponding latent states. We introduce a physics-informed learning objective for CNF-ROM, which includes two key components. First, the framework uses coordinate-based neural networks to calculate and minimize PDE residuals by computing spatial derivatives via automatic differentiation and applying the chain rule for time derivatives. Second, exact initial and boundary conditions (IC/BC) are imposed using approximate distance functions (ADFs) [Sukumar and Srivastava, CMAME, 2022]. However, ADFs introduce a trade-off as their second- or higher-order derivatives become unstable at the joining points of boundaries. To address this, we introduce an auxiliary network inspired by [Gladstone et al., NeurIPS ML4PS workshop, 2022]. Our method is validated through parameter extrapolation and interpolation, temporal extrapolation, and comparisons with analytical solutions.
Source: arXiv (Cornell University)
Authors: Kim, Minji, Wen, Tianshu, Lee, Kookjin, Choi, Youngsoo
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1088636562, G1356433355, G14554683, G2145270357, G217780377, G3390444915, G3669113783, G4094752214, CAREER: Accelerating Scientific Discovery via Deep Learning with Strong Physics Inductive Biases, CENTER FOR HIERARCHICAL AND ROBUST MODELING OF NON-EQUILIBRIUM TRANSPORT (CHARMNET), G5685548091, G574795485, G5946024249, G8397015973, G895790057, G991281326
OpenAlex ID: W4405172822