Data-driven modeling of shock physics by physics-informed MeshGraphNets

TL;DR

This work studies the Sedov Taylor shock propagation problem using a physics informed graph based surrogate model, Physics Informed MeshGraphNet (PhyMGN), designed for grid-based hydrodynamics, which is able to generalize beyond the training regime with a higher accuracy and preserves differentiability in parameter space while achieving a substantial reduction in computational cost relative to conventional numerical solvers.

Abstract

High-resolution fluid simulations for plasma physics and astrophysics rely on Particle in cell (PIC) and hydrodynamic solvers (e.g., FLASH) to resolve shock dominated, multiscale phenomena, but their high computational cost severely limits scalability. This motivates the development of learning based surrogate models, which offer a promising route to accelerate these simulations while preserving physical fidelity. In this work, we study the Sedov Taylor shock propagation problem using a physics informed graph based surrogate model, Physics Informed MeshGraphNet (PhyMGN), designed for grid-based hydrodynamics. By incorporating weak physics constraints derived from the Euler equations using finite difference method, the model captures the self similar shock evolution and associated flow structures without explicitly solving the full hydrodynamic equations at each timestep. Comparing to the baseline MeshGraphNet model, PhyMGN is able to generalize beyond the training regime with a higher accuracy and preserves differentiability in parameter space while achieving a substantial reduction in computational cost relative to conventional numerical solvers.

Figures (11)

• Figure 1: Diagram of Phy-MGN training process. The dataloader loads a batch of graph data into the trainer, where the node and edge features are concatenated and reconstructed into a graph object before being passed into the model. The model performs a forward pass and generates outputs that represent both the state dynamics and predicted future states. By combining these outputs with the input states, the complete state at the next time step is obtained, which can then be used within the governing PDE to compute spatial derivatives. The PDE residual, derived from these computations, serves as the physics-informed loss. Together with the data-driven loss, it forms the total loss function. This total loss is then backpropagated through the network to update the model parameters. The entire process is repeated iteratively until the training converges.
• Figure 2: Diagram of k-hop neighborhood. When message passing is applied k-times (k=2 here), each node aggregates information from all nodes within its k-hop neighborhood k-hopping.
• Figure 3: Diagram of Phy-MGN inference process. Phy-MGN consists of an Encoder-Processor-Decoder architecture. The encoder transforms input graph $\mathcal{G}_t$ into latent space, the processor performs several rounds of message passing, the decoder then computes the dynamics and future states to update input state, producing states and graph in the next timestep $\mathcal{G}_{t+1}$. This process is applied iteratively to produce predictions along inference time.
• Figure 4: Model predictions on an unseen test case. The figure above presents Phy-MGN and MGN predictions of density and x-velocity (U) for a sample with ambient density 19, a test case outside the training parameter space, shown at the 50th (top row) and 100th (bottom row) inference time steps. The model was trained on data processed with a smoothing algorithm. The comparison shows that both models interpolate reliably early in the rollout. By the 100th step, MGN accumulates noticeable errors, with a more distorted shock front and noisier velocity fields—while Phy-MGN prediction maintains a clearer ring structure and more coherent flow, showing improved stability at longer rollout times.
• Figure 5: The mean squared error (MSE) of the Sedov problem is plotted for both Phy-MGN and MGN across all four state variables: density, pressure, x-velocity U, and y-velocity V. The models are trained using smoothed data. The resulting colormap indicates that Phy-MGN maintains lower errors over a longer prediction horizon than MGN, demonstrating greater robustness to error accumulation during iterative rollout, and improvement in long term stability.