Related papers: Taylor-mode automatic differentiation for construc…
The port-Hamiltonian approach presents an energy-based modeling of dynamical systems with energy-conservative and energy-dissipative parts as well as an interconnection over the so-called ports. In this paper, we apply an operator splitting…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
TorchOptics is an open-source Python library for differentiable Fourier optics simulations, developed using PyTorch to enable GPU-accelerated tensor computations and automatic differentiation. It provides a comprehensive framework for…
In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to…
A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material…
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
We consider real scalar field theories whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential $V$. By means of an extension of the standard definition of M{\o}ller operator, we construct an isomorphism…
We introduce a general framework for deriving effective dynamics from arbitrary time-dependent generators, based on a systematic operator cumulant expansion. Unlike traditional approaches, which typically assume periodic or adiabatic…
An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter…
We present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear operator. The proposed method utilizes…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
In this paper, we report the results of our latest work on the automated generation of planning operators from human demonstrations, and we present some of our future research ideas. To automatically generate planning operators, our system…
We propose the Taylorformer for random processes such as time series. Its two key components are: 1) the LocalTaylor wrapper which adapts Taylor approximations (used in dynamical systems) for use in neural network-based probabilistic…
A recent method called Asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrodinger equation for the bistable potentials. Optimal…
We introduce (weighted) rational expressions to denote series over Cartesian products of monoids. To this end, we propose the operator $|$ to build multitape expressions such as $(a^+|x + b^+|y)^*$. We define expansions, which generalize…