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The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…

This work introduces a lean CNN (convolutional neural network) framework, with a drastically reduced number of fittable parameters (<81K) compared to the benchmarks in current literature, to capture the underlying low-computational cost…

Identifying causal relations among multi-variate time series is one of the most important elements towards understanding the complex mechanisms underlying the dynamic system. It provides critical tools for forecasting, simulations and…

We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, 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…

Convolutional neural networks (CNNs) have demonstrated their superiority in numerous computer vision tasks, yet their computational cost results prohibitive for many real-time applications such as pedestrian detection which is usually…

Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics…

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…

As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Convolutional Neural Networks (CNNs) are a standard approach for visual recognition due to their capacity to learn hierarchical representations from raw pixels. In practice, practitioners often choose among (i) training a compact custom CNN…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…

Neural approaches to sequence labeling often use a Conditional Random Field (CRF) to model their output dependencies, while Recurrent Neural Networks (RNN) are used for the same purpose in other tasks. We set out to establish RNNs as an…

The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…

Non-parametric episodic memory can be used to quickly latch onto high-rewarded experience in reinforcement learning tasks. In contrast to parametric deep reinforcement learning approaches in which reward signals need to be back-propagated…

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…

Neural processes (NPs) are models for transfer learning with properties reminiscent of Gaussian Processes (GPs). They are adept at modelling data consisting of few observations of many related functions on the same input space and are…

We propose Impatient Deep Neural Networks (DNNs) which deal with dynamic time budgets during application. They allow for individual budgets given a priori for each test example and for anytime prediction, i.e., a possible interruption at…