Related papers: Regularised Atomic Body-Ordered Permutation-Invari…
The conformational properties of linear alkanes, C$_n$H$_{2n+2}$, have been of intense interest for many years. Experiments and corresponding electronic structure calculations were first reported in the mid-2000s and continue to the present…
We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills…
Polynomial interpolation is an important component of many computational problems. In several of these computational problems, failure to preserve positivity when using polynomials to approximate or map data values between meshes can lead…
Machine learning interatomic potentials (MLIPs) provide an effective approach for accurately and efficiently modeling atomic interactions, expanding the capabilities of atomistic simulations to complex systems. However, a priori feature…
We explore different ways to simplify the evaluation of the smooth overlap of atomic positions (SOAP) many-body atomic descriptor [Bart\'{o}k et al., Phys. Rev. B 87, 184115 (2013)]. Our aim is to improve the computational efficiency of…
Machine learning interatomic potentials (MLIPs) enable the accurate simulation of materials at larger sizes and time scales, and play increasingly important roles in the computational understanding and design of materials. However, MLIPs…
We introduce a new class of machine learning interatomic potentials - fast General Two- and Three-body Potential (GTTP), which is as fast as conventional empirical potentials and require computational time that remains constant with…
Machine-learned interatomic potentials (MILPs) are rapidly gaining interest for molecular modeling, as they provide a balance between quantum-mechanical level descriptions of atomic interactions and reasonable computational efficiency.…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies)…
The operation of large-scale infrastructure networks requires scalable optimization schemes. To guarantee safe system operation, a high degree of feasibility in a small number of iterations is important. Decomposition schemes can help to…
Machine-learning interatomic potentials (MLIPs) have made a significant contribution to the recent progress in the fields of computational materials and chemistry due to the MLIPs' ability of accurately approximating energy landscapes of…
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Machine learning interatomic potentials (MLIPs) based on a large dataset obtained by density functional theory (DFT) calculation have been developed recently. This study gives both conceptual and practical bases for the high accuracy of…
We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing…
We propose a simple scheme to construct composition-dependent interatomic potentials for multicomponent systems that when superposed onto the potentials for the pure elements can reproduce not only the heat of mixing of the solid solution…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
We present a computational scheme for predicting the ligands that bind to a pocket of known structure. It is based on the generation of a general abstract representation of the molecules, which is invariant to rotations, translations and…
Admissible states in hyperbolic systems and related equations often form a convex invariant domain. Numerical violations of this domain can lead to loss of hyperbolicity, resulting in illposedness and severe numerical instabilities. It is…