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Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

Time series prediction with neural networks has been the focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and…

The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue,…

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…

Recent progress in imitation learning has been enabled by policy architectures that scale to complex visuomotor tasks, multimodal distributions, and large datasets. However, these methods often rely on learning from large amount of expert…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such…

Representation learning for high-dimensional, complex physical systems aims to identify a low-dimensional intrinsic latent space, which is crucial for reduced-order modeling and modal analysis. To overcome the well-known Kolmogorov barrier,…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

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…

We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…

We propose a novel machine learning strategy for studying neuroanatomical shape variation. Our model works with volumetric binary segmentation images, and requires no pre-processing such as the extraction of surface points or a mesh. The…

We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the…

Integrating domain knowledge into deep learning has emerged as a promising direction for improving model interpretability, generalization, and data efficiency. In this work, we present a novel knowledge-guided ViT-based Masked Autoencoder…