相关论文: Momentum-Accelerated Richardson(m) and Their Multi…

While memory-augmented neural networks (MANNs) offer an effective solution for few-shot learning (FSL) by integrating deep neural networks with external memory, the capacity requirements and energy overhead of data movement become enormous…

We describe a hybrid analog-digital computing approach to solve important combinatorial optimization problems that leverages memristors (two-terminal nonvolatile memories). While previous memristor accelerators have had to minimize analog…

This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

Edge computing for neural networks is getting important especially for low power applications and offline devices. TensorFlow Lite and PyTorch Mobile were released for this purpose. But they mainly support mobile devices instead of…

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual…

The aim is to justify rigorously the so-called reduced magnetohydrodynamic model (abbreviated as RMHD), which is widely used in fusion, space and astrophysical plasmas. Motivated by physics, the focus is on plasmas that are simultaneously…

Evaluation of pair potentials is critical in a number of areas of physics. The classicalN-body problem has its root in evaluating the Laplace potential, and has spawned tree-algorithms, the fast multipole method (FMM), as well as kernel…

Under the multiplicative noise scaling (MNS) condition, original Nesterov acceleration is provably sensitive to noise and may diverge when gradient noise overwhelms the signal. In this paper, we develop two accelerated stochastic gradient…

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…

In recent years, even though Stochastic Gradient Descent (SGD) and its variants are well-known for training neural networks, it suffers from limitations such as the lack of theoretical guarantees, vanishing gradients, and excessive…

In this paper we present a massively parallel open source solver for Richards equation, named the RichardsFOAM solver. This solver has been developed in the framework of the open source generalist computational fluid dynamics tool box…

Quantization is widely employed in both cloud and edge systems to reduce the memory occupation, latency, and energy consumption of deep neural networks. In particular, mixed-precision quantization, i.e., the use of different bit-widths for…

We introduce forward-backward stochastic differential equations, highlighting the connection between solutions of these and solutions of partial differential equations, related by the Feynman-Kac theorem. We review the technique of…

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

In orthogonal frequency division multiplexing (OFDM), accurate channel estimation is crucial. Classical signal processing-based approaches, such as linear minimum mean-squared error (LMMSE) estimation, often require second-order statistics…

Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator~(DeepONet) to…

The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to…

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…