Atomic Structure Relaxation via Segmented Minimization

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Solution Overview

Problem

Current ab initio simulation methods, such as those using the Vienna Ab-initio Simulation Package (VASP), face challenges in efficiently determining ab initio characteristics of atomic structures due to high computational costs and inaccuracies associated with fixed k-mesh resolutions and minimization algorithms, leading to either high computational expense or inaccurate results.

Innovation Solution

A system comprising a control module that iteratively transforms a model of an atomic structure using a combination of conjugate gradient and quasi-Newton minimization methods, along with varying k-mesh resolutions, to determine ab initio characteristics, including atomic forces, positions, and energy minimization, thereby avoiding saddle points and achieving accurate results with reduced computational burden.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Speed

If conjugate gradient minimization is used for atomic structure relaxation, then computational speed is improved, but accuracy deteriorates due to inability to avoid saddle points

Engineering Contradiction:
Improvecomputational speedVSAvoidaccuracy of ab initio characteristics
Core Design Contradiction:
SpeedVSMeasurement precision

Solution Approach 1:

The minimization process is divided into two distinct segments: first using conjugate gradient minimization for rapid initial relaxation to reach intermediate states, then using quasi-Newton minimization for final convergence to the ground state. This segmentation allows each method to operate in its optimal performance regime.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The conjugate gradient minimization performs preliminary relaxation actions to bring the atomic structure close to the minimum energy state before the quasi-Newton minimization takes over for final precision convergence. This preliminary action reduces the computational burden on the more accurate but slower quasi-Newton method.

Inventive Principle:
Principle #10Preliminary action

2Measurement precision

If high k-mesh resolution is used for Brillouin zone sampling, then measurement precision is improved, but computational cost increases

Engineering Contradiction:
Improveaccuracy of ab initio characteristicsVSAvoidcomputational cost
Core Design Contradiction:
Measurement precisionVSUse of energy by moving object

Solution Approach 1:

The conjugate gradient minimization with potentially lower k-mesh resolution performs preliminary structural relaxation, and only the final quasi-Newton minimization step uses high k-mesh resolution. This ensures high accuracy is achieved only when necessary for final convergence, reducing overall computational cost.

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

High k-mesh resolution is applied partially rather than throughout the entire minimization process. It is used selectively in the final convergence phase where maximum precision is needed, rather than excessively applying it to all intermediate steps where lower precision would suffice.

Inventive Principle:
Principle #16Partial or excessive action

3Device complexity

If fixed minimization algorithm is used, then device complexity is reduced, but adaptability deteriorates due to inability to handle different convergence requirements

Engineering Contradiction:
Improvealgorithm complexityVSAvoidadaptability to different convergence requirements
Core Design Contradiction:
Device complexityVSAdaptability or versatility

Solution Approach 1:

The minimization algorithm dynamically switches between conjugate gradient and quasi-Newton methods based on the convergence state of the atomic structure. The system adapts its computational approach automatically during the relaxation process, transitioning from rapid initial relaxation to precise final convergence as needed.

Inventive Principle:
Principle #15Dynamics

Solution Approach 2:

The algorithm changes its parameters (minimization method type) based on the progression of the relaxation process. Early stages use conjugate gradient parameters optimized for speed, while final stages switch to quasi-Newton parameters optimized for precision convergence, allowing the system to adapt to different convergence requirements at different stages.

Inventive Principle:
Principle #35Parameter changes

Data Source

PatentEP3380962B1Atomic structure optimization
Publication Date: 2024.02.14 SYNOPSYS INC
  • EP3380962B1 patent drawingFigure 1
  • EP3380962B1 patent drawingFigure 2~3
  • EP3380962B1 patent drawingFigure 4~5

AI summary

Electronic design automation modules simulate the behavior of structures and materials at atomic scale with parameters or a configuration that varies across iterative transformations.