Session
2026 Session 2
Location
Orem, UT
Start Date
5-4-2026 9:10 AM
Description
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in order to resolve the solution accurately, resulting in increased computational cost. In order to accelerate the simulation of these ODEs we present a novel methodology that uses a pseudo-invertible neural network to map system states into a high-dimensional latent space. The network is then trained so that the dynamics in this learned latent space are slow, and can be simulated with relatively few solver function calls. Unlike existing neural methods, the latent dynamic equations are not learned from trajectory data, but derived from the original system equations and the chain rule. This allows the method to generalize better than existing approaches because the derived equations are correct by construction. In this work, we derive latent state equations of motion for any general ODE, and describe the loss function used to enforce slow time evolution of the latent states. We then apply this technique to two example ODEs and show that these problems can be solved with 3x to 20x fewer function calls for the same accuracy when simulating in the learned latent space.
Accelerating Ordinary Differential Equations Through Physics-Preserving Neural Networks
Orem, UT
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in order to resolve the solution accurately, resulting in increased computational cost. In order to accelerate the simulation of these ODEs we present a novel methodology that uses a pseudo-invertible neural network to map system states into a high-dimensional latent space. The network is then trained so that the dynamics in this learned latent space are slow, and can be simulated with relatively few solver function calls. Unlike existing neural methods, the latent dynamic equations are not learned from trajectory data, but derived from the original system equations and the chain rule. This allows the method to generalize better than existing approaches because the derived equations are correct by construction. In this work, we derive latent state equations of motion for any general ODE, and describe the loss function used to enforce slow time evolution of the latent states. We then apply this technique to two example ODEs and show that these problems can be solved with 3x to 20x fewer function calls for the same accuracy when simulating in the learned latent space.