Related papers: Schrodinger AI: A Unified Spectral-Dynamical Frame…
The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
We present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems containing $2^n$ coupled oscillators (Eg: $2^n$ masses coupled by springs), including those with time-dependent forces, time-varying…
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the…
Spatiotemporal forecasting of complex three-dimensional phenomena (4D: 3D + time) is fundamental to applications in medical imaging, fluid and material dynamics, and geophysics. In contrast to unconstrained neural forecasting models, we…
We present a quantum computational framework that systematically converts classical linear iterative algorithms with fixed iteration operators into their quantum counterparts using the Schr\"odingerization technique [Shi Jin, Nana Liu and…
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…
We introduce Teleodynamic Learning, a new paradigm for machine learning in which learning is not the minimization of a fixed objective, but the emergence and stabilization of functional organization under constraint. Inspired by living…
Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it…
This paper introduces decentralized and modular neural network framework designed to enhance the scalability, interpretability, and performance of artificial intelligence (AI) systems. At the heart of this framework is a dynamic switch…
Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods.…
A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of…
Neurosymbolic artificial intelligence (AI) systems combine neural network and classical symbolic AI mechanisms to exploit the complementary strengths of large scale, generalizable learning and robust, verifiable reasoning. Numerous…
The unification of statistical (data-driven) and symbolic (knowledge-driven) methods is widely recognised as one of the key challenges of modern AI. Recent years have seen large number of publications on such hybrid neuro-symbolic AI…
We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts caused by different three-dimensional spherically symmetric potentials at fixed…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
This article discusses applications of Bayesian machine learning for quantum molecular dynamics. One particular formulation of quantum dynamics advocated here is in the form of a machine learning simulator of the Schr\"{o}dinger equation.…
Learning internal reasoning processes is crucial for developing AI systems capable of sustained adaptation in dynamic real-world environments. However, most existing approaches primarily emphasize learning task-specific outputs or static…