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Data-driven methods for modelling purposes in fluid mechanics are a promising alternative given the continuous increase of both computational power and data-storage capabilities. Highly non-linear flows including turbulence and reaction are…

Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.

We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…

Despite recent breakthroughs in the applications of deep neural networks, one setting that presents a persistent challenge is that of "one-shot learning." Traditional gradient-based networks require a lot of data to learn, often through…

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…

The shift to data-intensive processing from the cloud to the edge has introduced new challenges and expectations for the next generation of intelligent computing systems. As the memory wall continues to grow, modern systems can only meet…

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been…

Due to their great performance and scalability properties neural networks have become ubiquitous building blocks of many applications. With the rise of mobile and IoT, these models now are also being increasingly applied in distributed…

Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly…

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…

Non-equilibrium molecular-scale dynamics, where fast electron transport couples with slow chemical state evolution, underpins the complex behaviors of molecular memristors, yet a general model linking these dynamics to neuromorphic…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

Deep neural networks are increasingly used on mobile devices, where computational resources are limited. In this paper we develop CondenseNet, a novel network architecture with unprecedented efficiency. It combines dense connectivity with a…

Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…

As deep neural network (NN) methods have matured, there has been increasing interest in deploying NN solutions to "edge computing" platforms such as mobile phones or embedded controllers. These platforms are often resource-constrained,…

This paper proposes the Mesh Neural Network (MNN), a novel architecture which allows neurons to be connected in any topology, to efficiently route information. In MNNs, information is propagated between neurons throughout a state transition…

We developed analytical and numerical methods to study a transport of non-interacting particles in large networks consisting of M d-dimensional containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij} and radii a_{ij}…