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This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

Accurate prediction over long time horizons is crucial for modeling complex physical processes such as wave propagation. Although deep neural networks show promise for real-time forecasting, they often struggle with accumulating phase and…

A low-complexity convolutional neural network estimator which learns the minimum mean squared error channel estimator for single-antenna users was recently proposed. We generalize the architecture to the estimation of MIMO channels with…

Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient…

Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets…

Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful…

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…

In many neuromorphic workflows, simulators play a vital role for important tasks such as training spiking neural networks (SNNs), running neuroscience simulations, and designing, implementing and testing neuromorphic algorithms. Currently…

Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…

This paper proposes a method for reconstructing three-dimensional turbulent flows from sparse measurements without the need for ground truth data during training. A weight-sharing network is developed to infer the full flow fields from…

Neuron models built from experimental data have successfully predicted observed voltage oscillations within and beyond training range. A tantalising prospect is the possibility of estimating the unobserved dynamics of ion channels which is…

Low-count positron emission tomography (PET) reconstruction is a challenging inverse problem due to severe degradations arising from Poisson noise, photon scarcity, and attenuation correction errors. Existing deep learning methods typically…

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…

Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…

When training deep neural networks, keeping all tensors in high precision (e.g., 32-bit or even 16-bit floats) is often wasteful. However, keeping all tensors in low precision (e.g., 8-bit floats) can lead to unacceptable accuracy loss.…

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an…

Reinforcement learning augmented by the representational power of deep neural networks, has shown promising results on high-dimensional problems, such as game playing and robotic control. However, the sequential nature of these problems…

Predictive coding networks are neural models that perform inference through an iterative energy minimization process, whose operations are local in space and time. While effective in shallow architectures, they suffer significant…