Related papers: Towards a Foundation Model for Neural Network Wave…

Recent foundation models are capable of handling multiple tasks and multiple data modalities with the unified base model structure and several specialized model components. However, efficient training of such multi-task (MT) multi-modal…

We present an efficient classical algorithm based on the construction of a unitary quantum circuit for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions. Using an analogy with the massless Dirac equation, second…

This work presents exchange potentials for specific orbitals calculated by inverting Hartree-Fock wavefunctions. This was achieved by using a Depurated Inversion Method. The basic idea of the method relies upon the substitution of…

The success of deep neural networks has inspired many to wonder whether other learners could benefit from deep, layered architectures. We present a general framework called forward thinking for deep learning that generalizes the…

The increasing need for compact and low-power computing solutions for machine learning applications has triggered significant interest in energy-efficient neuromorphic systems. However, most of these architectures rely on spiking neural…

This paper examines the possibility of, and the possible advantages to learning the filters of convolutional neural networks (CNNs) for image analysis in the wavelet domain. We are stimulated by both Mallat's scattering transform and the…

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…

A core technology that has emerged from the artificial intelligence revolution is the recurrent neural network (RNN). Its unique sequence-based architecture provides a tractable likelihood estimate with stable training paradigms, a…

The Hartree-Fock exchange potential is fundamental for capturing quantum mechanical exchange effects but faces critical challenges in large-scale applications due to its nonlocal and computationally intensive nature. This study introduces a…

The practical utility of M{\o}ller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that use of regularized orbital-optimized MP2 orbitals and scaling of MP3…

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…

Modern deep learning usually treats models as separate artifacts: trained independently, specialized for particular purposes, and replaced when improved versions appear. This thesis studies model merging as an alternative paradigm:…

Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…

Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

High-order wave-making theories are becoming available but are limited to certain ranges of waves and wavemaker types in their applicability. Alternatively, machine learning can be considered to find nonlinear functional relationships.…

The integration of density functional theory (DFT) with machine learning enables efficient \textit{ab initio} electronic structure calculations for ultra-large systems. In this work, we develop a transfer learning framework tailored for…

Recently, it has been shown that neural networks not only approximate the ground-state wave functions of a single molecular system well but can also generalize to multiple geometries. While such generalization significantly speeds up…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

The intrinsic Helmholtz free-energy functional, the centerpiece of classical density functional theory, is at best only known approximately for 3D systems. Here we introduce a method for learning a neuralnetwork approximation of this…