Learning non-Markovian Dynamical Systems with Signature-based Encoders
This addresses the limitation of neural ODEs in handling memory effects for complex systems like continuous control, though it appears incremental as it builds on existing encoder-decoder models with a new encoding component.
The paper tackles the problem of modeling non-Markovian dynamical systems, which depend on historical states, by proposing a signature-based encoder as a continuous-time alternative to RNN-based methods, and demonstrates that it outperforms RNN-based alternatives on synthetic benchmarks.
Neural ordinary differential equations offer an effective framework for modeling dynamical systems by learning a continuous-time vector field. However, they rely on the Markovian assumption - that future states depend only on the current state - which is often untrue in real-world scenarios where the dynamics may depend on the history of past states. This limitation becomes especially evident in settings involving the continuous control of complex systems with delays and memory effects. To capture historical dependencies, existing approaches often rely on recurrent neural network (RNN)-based encoders, which are inherently discrete and struggle with continuous modeling. In addition, they may exhibit poor training behavior. In this work, we investigate the use of the signature transform as an encoder for learning non-Markovian dynamics in a continuous-time setting. The signature transform offers a continuous-time alternative with strong theoretical foundations and proven efficiency in summarizing multidimensional information in time. We integrate a signature-based encoding scheme into encoder-decoder dynamics models and demonstrate that it outperforms RNN-based alternatives in test performance on synthetic benchmarks.