DEM-NeRF: A Neuro-Symbolic Method for Scientific Discovery through Physics-Informed Simulation
This addresses the challenge of high-fidelity physics simulations for scientific discovery, though it appears incremental as it builds on existing neuro-symbolic and PINN methods.
The authors tackled the problem of reconstructing and simulating elastic objects from sparse multi-view image sequences without explicit geometric information, by integrating neural radiance fields with physics-informed neural networks, resulting in enhanced simulation accuracy and explainability.
Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, neuro-symbolic approaches that combine data-driven learning, the neuro, with symbolic equations and rules, the symbolic, address the tension between methods that are purely empirical, which risk straying from established physical principles, and traditional numerical solvers that demand complete geometric knowledge and can be prohibitively expensive for high-fidelity simulations. In this work, we present a novel neuro-symbolic framework for reconstructing and simulating elastic objects directly from sparse multi-view image sequences, without requiring explicit geometric information. Specifically, we integrate a neural radiance field (NeRF) for object reconstruction with physics-informed neural networks (PINN) that incorporate the governing partial differential equations of elasticity. In doing so, our method learns a spatiotemporal representation of deforming objects that leverages both image supervision and symbolic physical constraints. To handle complex boundary and initial conditions, which are traditionally confronted using finite element methods, boundary element methods, or sensor-based measurements, we employ an energy-constrained Physics-Informed Neural Network architecture. This design enhances both simulation accuracy and the explainability of results.