DEM-NeRF: A Neuro-Symbolic Method for Scientific Discovery through Physics-Informed Simulation

TL;DR

This paper introduces DEM-NeRF, a neuro-symbolic framework combining neural radiance fields and physics-informed neural networks to reconstruct and simulate elastic objects from sparse images, integrating physical laws for accurate, explainable modeling.

Contribution

The work presents a novel neuro-symbolic approach that reconstructs and simulates elastic objects directly from images without explicit geometry, integrating PDEs into neural networks for physical consistency.

Findings

Successfully reconstructs elastic objects from sparse multi-view images.

Integrates PDE constraints into neural networks for physics-based simulation.

Enhances simulation accuracy and explainability through energy-constrained PINNs.

Abstract

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.