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The recurrent neural networks (RNN) with richly distributed internal states and flexible non-linear transition functions, have overtaken the dynamic Bayesian networks such as the hidden Markov models (HMMs) in the task of modeling highly…

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…

A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Deep latent variable models, trained using variational autoencoders or generative adversarial networks, are now a key technique for representation learning of continuous structures. However, applying similar methods to discrete structures,…

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

This paper develops tools to obtain robust probabilistic estimates for queueing models at the large deviations (LD) scale. These tools are based on the recently introduced robust R\'enyi bounds, which provide LD estimates (and more…

Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…

Noting the importance of factorizing (or disentangling) the latent space, we propose a novel, non-probabilistic disentangling framework for autoencoders, based on the principles of symmetry transformations in group-theory. To the best of…

Time-series anomaly detection plays a vital role in monitoring complex operation conditions. However, the detection accuracy of existing approaches is heavily influenced by pattern distribution, existence of multiple normal patterns,…

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the…

Real-world robots must operate under evolving dynamics caused by changing operating conditions, external disturbances, and unmodeled effects. These may appear as gradual drifts, transient fluctuations, or abrupt shifts, demanding real-time…

Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…