Breaking Free: Decoupling Forced Systems with Laplace Neural Networks

Abstract

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.