Physics-informed reduced order model with conditional neural fields

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].