Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methods
This addresses a barrier to widespread adoption of neural ODEs in science and engineering by improving efficiency for stiff systems, though it is incremental as it builds on earlier work.
The paper tackled the problem of training stiff neural ordinary differential equations (ODEs) by exploring explicit exponential integration methods as a more efficient alternative to implicit methods, finding that the integrating factor Euler method succeeded in training the stiff Van der Pol oscillator where implicit schemes failed, even with large step sizes.
Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of neural ODEs. In our earlier work, we addressed this challenge by utilizing single-step implicit methods for solving stiff neural ODEs. While effective, these implicit methods are computationally costly and can be complex to implement. This paper expands on our earlier work by exploring explicit exponential integration methods as a more efficient alternative. We evaluate the potential of these explicit methods to handle stiff dynamics in neural ODEs, aiming to enhance their applicability to a broader range of scientific and engineering problems. We found the integrating factor Euler (IF Euler) method to excel in stability and efficiency. While implicit schemes failed to train the stiff Van der Pol oscillator, the IF Euler method succeeded, even with large step sizes. However, IF Euler's first-order accuracy limits its use, leaving the development of higher-order methods for stiff neural ODEs an open research problem.