Multiobjective Differential Evolution for Higher-Dimensional Multimodal Multiobjective Optimization

In multimodal multiobjective optimization problems(MMOPs),there are several Pareto optimal solutions corre-sponding to the identical objective vector.This paper proposes a new differential evolution algorithm to solve MMOPs with higher-dimensional decision variables.Due to the increase in the dimensions of decision variables in real-world MMOPs,it is diffi-cult for current multimodal multiobjective optimization evolu-tionary algorithms(MMOEAs)to find multiple Pareto optimal solutions.The proposed algorithm adopts a dual-population framework and an improved environmental selection method.It utilizes a convergence archive to help the first population improve the quality of solutions.The improved environmental selection method enables the other population to search the remaining decision space and reserve more Pareto optimal solutions through the information of the first population.The combination of these two strategies helps to effectively balance and enhance conver-gence and diversity performance.In addition,to study the per-formance of the proposed algorithm,a novel set of multimodal multiobjective optimization test functions with extensible decision variables is designed.The proposed MMOEA is certified to be effective through comparison with six state-of-the-art MMOEAs on the test functions.

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics(MD)has served as a powerful tool for designing materials with reduced reliance on laboratory testing.However,the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach.In this work,we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets.Firstly,we develop a novel coarse-graining method,to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets.Inspired by the weighted essentially non-oscillatory(WENO)scheme,the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil,then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities.Then,based on the coarse-grained MD data,a two-phase optimizationbased learning approach is proposed to infer the optimal peridynamics model with damage criterion.In the first phase,we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties.Then,in the second phase,the material damage criterion is learnt as a smoothed step function from the data with fractures.As a result,a peridynamics surrogate is obtained.As a continuum model,our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training,and hence allows for substantial reductions in computational cost compared with MD.We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene.Our tests show that the proposed data-driven model is robust and generalizable,in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

Performant implementation of the atomic cluster expansion(PACE)and application to copper and silicon

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions.Here we implement the atomic cluster expansion in the performant C++code PACE that is suitable for use in large-scale atomistic simulations.We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation.We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations.Moreover,general purpose parameterizations are presented for copper and silicon and evaluated in detail.We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

Trajectory sampling and finite-size effects in first-principles stopping power calculations

Real-time time-dependent density functional theory(TDDFT)is presently the most accurate available method for computing electronic stopping powers from first principles.However,obtaining application-relevant results often involves either costly averages over multiple calculations or ad hoc selection of a representative ion trajectory.We consider a broadly applicable,quantitative metric for evaluating and optimizing trajectories in this context.This methodology enables rigorous analysis of the failure modes of various common trajectory choices in crystalline materials.Although randomly selecting trajectories is common practice in stopping power calculations in solids,we show that nearly 30%of random trajectories in an FCC aluminum crystal will not representatively sample the material over the time and length scales feasibly simulated with TDDFT,and unrepresentative choices incur errors of up to 60%.We also show that finite-size effects depend on ion trajectory via“ouroboros”effects beyond the prevailing plasmon-based interpretation,and we propose a cost-reducing scheme to obtain converged results even when expensive core-electron contributions preclude large supercells.This work helps to mitigate poorly controlled approximations in first-principles stopping power calculations,allowing 1–2 order of magnitude cost reductions for obtaining representatively averaged and converged results.

Predicting electronic structures at any length scale with machine learning

The properties of electrons in matter are of fundamental importance.They give rise to virtually all material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant gas planets.Modeling and simulation of such diverse applications rely primarily on density functional theory(DFT),which has become the principal method for predicting the electronic structure of matter.While DFT calculations have proven to be very useful,their computational scaling limits them to small systems.We have developed a machine learning framework for predicting the electronic structure on any length scale.It shows up to three orders of magnitude speedup on systems where DFT is tractable and,more importantly,enables predictions on scales where DFT calculations are infeasible.Our work demonstrates how machine learning circumvents a long-standing computational bottleneck and advances materials science to frontiers intractable with any current solutions.

Unsupervised WSD by Finding the Predominant Sense Using Context as a Dynamic Thesaurus

We present and analyze an unsupervised method for Word Sense Disambiguation（WSD）.Our work is based on the method presented by McCarthy et al.in 2004 for finding the predominant sense of each word in the entire corpus.Their maximization algorithm allows weighted terms（similar words） from a distributional thesaurus to accumulate a score for each ambiguous word sense,i.e.,the sense with the highest score is chosen based on votes from a weighted list of terms related to the ambiguous word.This list is obtained using the distributional similarity method proposed by Lin Dekang to obtain a thesaurus.In the method of McCarthy et al.,every occurrence of the ambiguous word uses the same thesaurus,regardless of the context where the ambiguous word occurs.Our method accounts for the context of a word when determining the sense of an ambiguous word by building the list of distributed similar words based on the syntactic context of the ambiguous word.We obtain a top precision of 77.54%of accuracy versus 67.10%of the original method tested on SemCor.We also analyze the effect of the number of weighted terms in the tasks of finding the Most Precuent Sense（MFS） and WSD,and experiment with several corpora for building the Word Space Model.