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Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…

This paper presents a spike-based model which employs neurons with functionally distinct dendritic compartments for classifying high dimensional binary patterns. The synaptic inputs arriving on each dendritic subunit are nonlinearly…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Optimizing a high-dimensional non-convex function is, in general, computationally hard and many problems of this type are hard to solve even approximately. Complexity theory characterizes the optimal approximation ratios achievable in…

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

This work proposes RaNNC (Rapid Neural Network Connector) as middleware for automatic hybrid parallelism. In recent deep learning research, as exemplified by T5 and GPT-3, the size of neural network models continues to grow. Since such…

Deep Reinforcement Learning (DRL) has emerged as a powerful model-free paradigm for learning optimal policies. However, in navigation tasks with cluttered environments, DRL methods often suffer from insufficient exploration, especially…

We propose an optimization-based approach to plan power grasps. Central to our method is a reformulation of grasp planning as an infinite program under complementary constraints (IPCC), which allows contacts to happen between arbitrary…

We propose a novel deep learning (DL) approach to solve one-dimensional non-linear elliptic, parabolic, and hyperbolic problems on graphs. A system of physics-informed neural network (PINN) models is used to solve the differential…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

The success of deep learning is due, to a large extent, to the remarkable effectiveness of gradient-based optimization methods applied to large neural networks. The purpose of this work is to propose a modern view and a general mathematical…

Large language models (LLMs) have demonstrated strong performance on coding tasks such as generation, completion and repair, but their ability to handle complex symbolic reasoning over code still remains underexplored. We introduce the task…

Deep reinforcement learning has the potential to address various scientific problems. In this paper, we implement an optics simulation environment for reinforcement learning based controllers. The environment captures the essence of…

The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It…

Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…

Parkinson's disease is marked by altered and increased firing characteristics of pathological oscillations in the brain. In other words, it causes abnormal synchronous oscillations and suppression during neurological processing. In order to…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…