In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This st...In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.展开更多
Machine learning(ML)surrogate models offer a promising route to accelerate material property prediction,bypassing costly atomistic simulations.Here,we introduce IsothermODE,a neural ordinary differential equation(NODE...Machine learning(ML)surrogate models offer a promising route to accelerate material property prediction,bypassing costly atomistic simulations.Here,we introduce IsothermODE,a neural ordinary differential equation(NODE)framework for reconstructing full uptake and heat of adsorption(ΔH_(ads))isotherms for CO_(2)adsorption in metal-organic frameworks(MOFs)using only sparse pressure data.Unlike traditional ML models,IsothermODE leverages the intrinsic structure of differential equations to produce smooth,physically-consistent predictions that generalize across wide pressure ranges.We demonstrate high-fidelity interpolation and extrapolation,even with only five pressure points.To address the stochasticity inherent in Grand Canonical Monte Carlo(GCMC)simulations,we integrate uncertainty quantification,yielding tight bounds on predicted enthalpy curves.We further interpret the learned latent dynamics in terms of adsorption thermodynamics and textural properties,offering insight into structure-property relationships.Finally,we demonstrate IsothermODE’s long-range interpolation and extrapolation capabilities with sparse isotherm data(5 pressure points)and large incomplete intervals featuring missing data between 4–40(case 1)and 25–50(case 2)bars.IsothermODE provides a fast,robust alternative to simulation-heavy workflows,enabling scalable screening and design of next-generation carbon capture materials.展开更多
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.10902076)the Natural Science Foundation of Shanxi Province of China(Grant No.2007011009)+1 种基金the Scientific Research and Development Program of the Shanxi Higher Education Institutions(Grant No.20091131)the Doctoral Startup Foundation of Taiyuan University of Science and Technology(Grant No.200708)
文摘In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.
基金the Engaging OnDemand clusters at MIT Office of Research Computing and Data (ORCD) and MIT SuperCloud. This work additionally used Bridges-2 at Pittsburgh Supercomputing Center (PSC) through allocation MCH230021 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation Grants No. 2138259, 2138286, 2138307, 2137603, and 2138296E.L. is supported by the National Science Foundation Graduate Research Fellowship under Grant No. 2141064.
文摘Machine learning(ML)surrogate models offer a promising route to accelerate material property prediction,bypassing costly atomistic simulations.Here,we introduce IsothermODE,a neural ordinary differential equation(NODE)framework for reconstructing full uptake and heat of adsorption(ΔH_(ads))isotherms for CO_(2)adsorption in metal-organic frameworks(MOFs)using only sparse pressure data.Unlike traditional ML models,IsothermODE leverages the intrinsic structure of differential equations to produce smooth,physically-consistent predictions that generalize across wide pressure ranges.We demonstrate high-fidelity interpolation and extrapolation,even with only five pressure points.To address the stochasticity inherent in Grand Canonical Monte Carlo(GCMC)simulations,we integrate uncertainty quantification,yielding tight bounds on predicted enthalpy curves.We further interpret the learned latent dynamics in terms of adsorption thermodynamics and textural properties,offering insight into structure-property relationships.Finally,we demonstrate IsothermODE’s long-range interpolation and extrapolation capabilities with sparse isotherm data(5 pressure points)and large incomplete intervals featuring missing data between 4–40(case 1)and 25–50(case 2)bars.IsothermODE provides a fast,robust alternative to simulation-heavy workflows,enabling scalable screening and design of next-generation carbon capture materials.
