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Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…

Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance…

Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…

Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

A convolutional neural network can be constructed using numerical methods for solving dynamical systems, since the forward pass of the network can be regarded as a trajectory of a dynamical system. However, existing models based on…

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

Time-reversal symmetry, which requires that the dynamics of a system should not change with the reversal of time axis, is a fundamental property that frequently holds in classical and quantum mechanics. In this paper, we propose a novel…

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical…

Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…

Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard…

Almost all real-world networks are subject to constant evolution, and plenty of evolving networks have been investigated to uncover the underlying mechanisms for a deeper understanding of the organization and development of them. Compared…

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

Neural Ordinary Differential Equations (Neural ODEs), as a novel category of modeling big data methods, cleverly link traditional neural networks and dynamical systems. However, it is challenging to ensure the dynamics system reaches a…

We introduce a method for learning the dynamics of complex nonlinear systems based on deep generative models over temporal segments of states and actions. Unlike dynamics models that operate over individual discrete timesteps, we learn the…