Modeling dynamical systems with complex interactions remains a significant challenge in computational science. While data-driven approaches offer flexibility, they often fail to respect fundamental physical laws, leading to poor generalization and energy drift over long time horizons. Although physics-informed learning, specifically Hamiltonian Neural Networks (HNNs), addresses this by enforcing a symplectic structure on the prediction vector field, standard HNNs are ill-equipped to handle real-world dissipative systems characterized by friction and external forces. Furthermore, training these networks us- ing iterative backpropagation is often computationally expensive and sensitive to hyper-parameter tuning. To address these limitations, this work introduces the Random Dissipative Hamiltonian Neural Networks (RDHNN), a framework that combines structure-preserving deep learning with the non-iterative Sampling Where It Matters (SWIM) al- gorithm. By decomposing the vector field into conservative and dissipative components, the RDHNN simultaneously learns the Hamiltonian and a dissipative function. The network constructs hidden layer activations from sampled data points and computes output weights analytically which eliminates the need for iterative optimization. We evaluate the performance of RDHNN and a parameter efficient variant, the SharedRDHNN, on benchmark dynamical systems including the damped single and double pendulums, mass-spring systems, RLC circuits and Duffing and Morse oscillators. The proposed framework demonstrates extreme training efficiency and achieves speedup factors of over five orders of magnitude compared to Adam optimization while maintaining trajectory prediction accuracy comparable to or better than that of standard neural networks and HNNs. Furthermore, since it explicitly decomposes the system into conservative and dissipative terms, it provides interpretable insights into the dynamical contributions of separate components rather than functioning as a black box approximator.     «

Modeling dynamical systems with complex interactions remains a significant challenge in computational science. While data-driven approaches offer flexibility, they often fail to respect fundamental physical laws, leading to poor generalization and energy drift over long time horizons. Although physics-informed learning, specifically Hamiltonian Neural Networks (HNNs), addresses this by enforcing a symplectic structure on the prediction vector field, standard HNNs are ill-equipped to handle real...     »