Latent dynamics networks predict evolving physical systems from varying starts
Learning PDE solution operators with variable initial conditions via Latent Dynamics Networks
Machine Learning
Summary
Simulating complex physical systems like fluids or materials can be very slow when using traditional methods. The authors improve a type of neural network called Latent Dynamics Network so it can handle different starting conditions for these systems. Their approach quickly learns from early observations and makes accurate predictions about how the system evolves over time. This helps create faster, adaptable models for many simulations without needing detailed spatial data. Their method works across several physical phenomena and keeps predictions accurate even with less detailed input measurements.
What this means in practice
- •For engineering simulation teams: Use the improved network to rapidly generate accurate simulations of physical systems starting from different initial states, reducing reliance on costly solvers.
- •For weather and climate modelers: Incorporate this approach to produce high-resolution predictions from sparse early-time data, enabling efficient forecasts across varying initial meteorological conditions.
Authors
Stefano Maria Pizzamiglio, Stefano Pagani, Francesco Regazzoni
Abstract
In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governed by Partial Differential Equations (PDEs). In this context, the Latent Dynamics Network (LDNet) has recently demonstrated remarkable performance in predicting the response of spatio-temporal systems, combining Neural Ordinary Differential Equations with nonlinear dimensionality reduction. However, the original formulation assumes a fixed initial condition, limiting its applicability to many real-world applications where a system evolves from varying starting states. In this work, we overcome this limitation while keeping the end-to-end training procedure of the original LDNet and its encoder-free nature, which preserves its intrinsic independence from spatial resolution and grid topology. We infer the initial latent state directly from a small set of early-time observations, treating latent-state initialization as an adaptation problem, and investigate two strategies: an auto-decoding formulation and a meta-learning approach in which the initial latent state acts as a task-specific context variable. We demonstrate the accuracy of the proposed methods across diverse physical phenomena, spanning advection-diffusion, fluid dynamics, and solid mechanics. Meta-learning markedly accelerates latent-state inference and induces smoother, better-conditioned optimization landscapes, and spontaneously organizes the latent space into a structured representation that reflects physically meaningful features of the underlying dynamics. The coordinate-based decoder enables training from spatially subsampled data while recovering high-resolution solution fields at inference. The resulting approach provides an efficient and resolution-independent surrogate modeling framework for many-query simulations of time-dependent PDEs with varying initial conditions.