Breaking Free: Decoupling Forced Systems with Laplace Neural Networks
This work addresses a critical challenge in domains like engineering and finance by enabling more flexible and interpretable modeling of forced systems, though it appears incremental as it builds on existing neural and theoretical concepts.
The paper tackles the problem of modeling forced dynamical systems with external inputs by proposing Laplace-Net, a decoupled neural framework that improves accuracy and robustness, achieving state-of-the-art results on eight benchmark datasets including linear, non-linear, and delayed systems.
Modelling forced dynamical systems - where an external input drives the system state - is critical across diverse domains such as engineering, finance, and the natural sciences. In this work, we propose Laplace-Net, a decoupled, solver-free neural framework for learning forced and delay-aware systems. It leverages a Laplace transform-based approach to decompose internal dynamics, external inputs, and initial values into established theoretical concepts, enhancing interpretability. Laplace-Net promotes transferability since the system can be rapidly re-trained or fine-tuned for new forcing signals, providing flexibility in applications ranging from controller adaptation to long-horizon forecasting. Experimental results on eight benchmark datasets - including linear, non-linear, and delayed systems - demonstrate the method's improved accuracy and robustness compared to state-of-the-art approaches, particularly in handling complex and previously unseen inputs.