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

2025-07-28

AI Summary

This work addresses the problem of reconstructing and physically consistent simulating deformable objects from sparse multi-view images without geometric priors. We propose a neuro-symbolic fusion framework that embeds symbolic constraints—namely, the partial differential equations of elastic mechanics and energy conservation laws—into a physics-informed neural network (PINN), tightly coupled with a neural radiance field (NeRF) for joint implicit modeling of geometry and appearance. The method requires no explicit mesh, dedicated sensors, or assumptions about initial shape, directly learning spatiotemporally continuous deformation fields from sparse-view imagery. Key contributions include: (1) a differentiable, energy-minimization-based physical constraint mechanism; and (2) a co-optimization architecture integrating PINN and NeRF to handle complex boundary and initial conditions. Experiments demonstrate high-fidelity reconstruction and strong physical consistency even under extremely low observation density, significantly reducing reliance on conventional geometric modeling.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

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.

Problem

• Reconstructing elastic objects from sparse multi-view images
• Integrating neural networks with physics-informed simulations
• Handling complex boundary conditions without explicit geometry

Innovation

• Neuro-symbolic framework for elastic object reconstruction
• NeRF and PINN integration for physics-informed simulation
• Energy-constrained PINN for complex boundary conditions