Related papers: DYNAMITE: A high-performance framework for solving…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

Image classification serves as the cornerstone of computer vision, traditionally achieved through discriminative models based on deep neural networks. Recent advancements have introduced classification methods derived from generative…

Dynamic multi-objective optimization (DMOO) has recently attracted increasing interest from both academic researchers and engineering practitioners, as numerous real-world applications that evolve over time can be naturally formulated as…

Dynamic environments pose great challenges for expensive optimization problems, as the objective functions of these problems change over time and thus require remarkable computational resources to track the optimal solutions. Although…

Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…

Digital Memcomputing machines (DMMs) are dynamical systems with memory (time non-locality) that have been designed to solve combinatorial optimization problems. Their corresponding ordinary differential equations depend on a few…

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon…

We implemented the charge self-consistent combination of Density Functional Theory and Dynamical Mean Field Theory (DMFT) in two full-potential methods, the Augmented Plane Wave and the Linear Muffin-Tin Orbital methods. We categorize the…

A critical bottleneck in deep reinforcement learning (DRL) is sample inefficiency, as training high-performance agents often demands extensive environmental interactions. Model-based reinforcement learning (MBRL) mitigates this by building…

Deep learning has proven to be a highly effective tool for a wide range of applications, significantly when leveraging the power of multi-loss functions to optimize performance on multiple criteria simultaneously. However, optimal selection…

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex…

Incomplete multi-modal medical image segmentation faces critical challenges from modality imbalance, including imbalanced modality missing rates and heterogeneous modality contributions. Due to their reliance on idealized assumptions of…

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM),…

We develop the extended dynamical mean field theory (E-DMFT) with a view towards realistic applications. {\bf 1)} We introduce an intuitive derivation of the E-DMFT formalism. By identifying the Hartree contributions before the E-DMFT…

The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

Neural Stochastic Differential Equations (Neural SDEs) provide a principled framework for modeling continuous-time stochastic processes and have been widely adopted in fields ranging from physics to finance. Recent advances suggest that…

We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions.…