Poster
in
Workshop: NeurIPS 2024 Workshop: Machine Learning and the Physical Sciences
Physics-informed reduced order model with conditional neural fields
Minji Kim · Tianshu Wen · Kookjin Lee · Youngsoo Choi
We address the challenge of approximating parametrized partial differential equation (PDE) solutions by extending the conditional neural fields (CNFs) framework to support both data-driven and physics-informed learning. We integrate CNFs into the physics-informed neural network (PINN) framework. Additionally, we impose exact initial and boundary conditions using approximate distance functions (ADFs) [Sukumar and Srivastava, CMAME, 2022], optimizing the learning process without requiring an encoding step. Our method is validated through parameter extrapolation and interpolation, temporal extrapolation, and comparisons with exact solutions. However, a trade-off arises with the use of ADFs, as they can result in unstable second derivatives near boundaries. We address this issue by introducing auxiliary networks following [Gladstone et al., NeurIPS ML4PS workshop, 2022].