Forecasting the behaviour of industrial robots, power grids or pandemics under changing external inputs requires accurate dynamical models that can adapt to varying signals and capture long-term effects such as delays or memory. While recent neural approaches address some of these challenges individually, their reliance on computationally intensive solvers and their black-box nature limit their practical utility. In this work, we propose Laplace-Net, a decoupled, solver-free neural framework for learning forced and delay-aware dynamical systems. It uses the Laplace transform to (i) bypass computationally intensive solvers, (ii) enable the learning of delays and memory effects and (iii) decompose each system into interpretable control-theoretic components. Laplace-Net also enhances transferability, as its modular structure allows for targeted re-training of individual components to new system setups or environments. Experimental results on eight benchmark datasets–including linear, nonlinear 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.