Neural Network-Based Surrogate Models of Lagrangian Continuum Simulators

The simulation of fluid and deformable solid dynamics is a cornerstone in disciplines ranging from engineering and environmental modeling to computer graphics and virtual reality. Traditional computational methods, despite their power, often struggle to balance accuracy, efficiency, and scalability, particularly in real-time and large-scale applications. This thesis addresses these challenges by developing neural network-based surrogate models specifically tailored for Lagrangian continuum simulations.

The research explores temporal learning within continuum simulations, starting with an in-depth analysis of encoding and decoding techniques that transform Euclidean coordinate-based continuum data into latent space representations. This transformation is essential for training neural networks to accurately model complex physical phenomena. The study systematically compares traditional time series prediction methods with advanced neural architectures, such as Long Short-Term Memory (LSTM) networks. Experimental results demonstrate that LSTM networks, when combined with Multi-Layer Perceptrons (MLP), significantly outperform traditional methods in capturing the intricate multi-material interactions and long-term dependencies inherent in Lagrangian simulations.

A key contribution of this research is the introduction of a Self-Supervised Graph Attention Operator, which enhances the neural network’s ability to capture and conserve critical physical properties like vorticity and energy across simulated particles. This operator enables accurate and stable predictions of complex fluid and deformable solid dynamics, overcoming the limitations of existing surrogate models that often compromise between computational efficiency and physical accuracy. Rigorous evaluations, including long-term stability tests and comparative analyses with traditional methods, demonstrate that the proposed models advance the state-of-the-art in surrogate modeling for continuum simulations.