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Although optimal control problems of dynamical systems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. In this Letter we present a…

In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the universal approximation properties of SA-NODEs for dynamical…

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…

Neural controlled differential equations (NCDEs), which are continuous analogues to recurrent neural networks (RNNs), are a specialized model in (irregular) time-series processing. In comparison with similar models, e.g., neural ordinary…

There has been a significant focus on modelling emotion ambiguity in recent years, with advancements made in representing emotions as distributions to capture ambiguity. However, there has been comparatively less effort devoted to the…

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…

We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…

Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…

Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

We present a falsification framework that integrates learned surrogate dynamics with optimal control to efficiently generate counterexamples for cyber-physical systems specified in signal temporal logic (STL). The unknown system dynamics…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

Stability guarantees are crucial when ensuring that a fully autonomous robot does not take undesirable or potentially harmful actions. We recently proposed the Neural Contractive Dynamical Systems (NCDS), which is a neural network…

To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…