Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations

TL;DR

The paper tackles the computational burden of high-fidelity 3D scalar transport simulations by proposing a differentiable hybrid physics–neural surrogate that projects the problem onto a 2D plane and learns a non-Markovian neural closure together with an updated, orthotropic diffusivity. The solver-in-loop architecture combines a physics-based finite-volume solver with a memory-enabled CNN closure and an LSTM, enabling accurate, long-horizon predictions with data efficiency (training on as few as 26 full-field simulations). Key findings include substantial runtime reductions (hours to under a minute), improved long-time accuracy due to memory, and strong generalization to moving-source scenarios with a final Spearman correlation of $0.96$, demonstrating the utility of memory-augmented, physics-guided surrogates for coarse-grained transport phenomena. The work provides a path toward fast, physically consistent surrogates for complex indoor transport problems and similar multi-scale systems, with potential for rapid scenario exploration and design optimization.

Abstract

Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts scalar transport in a complex domain orders of magnitude faster than the 3D simulation (from hours to less than 1 min). This end-to-end differentiable framework jointly learns the physical model parameterization (i.e. orthotropic diffusivity) and a non-Markovian neural closure model to capture unresolved, 'coarse-grained' effects, thereby enabling stable, long time horizon rollouts. This proposed model is data-efficient (learning with 26 training data), and can be flexibly extended to an out-of-distribution scenario (with a moving source), achieving a Spearman correlation coefficient of 0.96 at the final simulation time. Overall results show that this differentiable physics-neural framework enables fast, accurate, and generalizable coarse-grained surrogates for physical phenomena.

Figures (13)

• Figure 1: Schematic of time advancement scheme in the proposed hybrid physics-neural model. Dotted lines indicate the flow of hidden state and concentration field from each time step to the next.
• Figure 2: Velocity fields and turbulent diffusivity field (computed as $\nu_t/Sc_t$, where $\nu_t$ is the turbulent viscosity and $Sc_t=0.9$ is the turbulent Schmidt number) as extracted from the full 3D numerical simulation
• Figure 3: Comparison of $L_{data}$ and MSE against flow time for the (Left) training and (Right) test datasets, with different lines indicating results after each stage of curriculum learning (i.e. after being trained with 60s, 120s, 300s, 600s of flow time respectively). Loss is averaged over all different release locations of the training and test dataset respectively.
• Figure 4: Learned diffusivity with some learned features circled in red and learned closure term. (a) Layout of room, with air-cons and pillars labeled as red and grey boxes respectively. (b) Sample closure term from a time point towards the end of the simulation time. Learned diffusivity along (c) x-direction and (d) y-direction. Yellow, green and blue indicate areas of high, medium and low diffusivity respectively. Low diffusivity regions (e.g. blue-black regions) can result if there are structural obstructions (e.g. internal pillars or walls).
• Figure 5: Comparison of $L_{data}$ and MSE against flow time for the (Left) training and (Right) test datasets, based on the physics-neural model and a solely data-driven approach. Errors are averaged over different release locations of the training and test datasets.