H-Rサンプリングと局所接空間の貼り合わせによる 三次元ラプラシアン平滑化制約を活用した 解探索空間のatlas型次元削減法
DOI:
https://doi.org/10.51094/jxiv.4615キーワード:
平滑化制約、 H-Rサンプリング、 三線形補間式、 多様体平坦化、 局所接空間、 大域 latent,、 ヒューリスティック探索抄録
非線形性が高く,感度算定が困難な物性同定問題でよく使用されるヒューリスティック探索手法には,次元の増加に弱く,変数次元が少し増えただけでも解探索性能が大幅に劣化するという課題がある.本稿では人が外部情報の概要を認知する仕組みをヒントに,可行点領域の特徴量を次元圧縮した空間上で解探索する手法を構築した.本手法では,まずH-Rサンプリングを用いて可行点領域の概略形状を捉えた後,元座標空間のサンプルを複数の局所接空間により局所的に低次元化し,それらの chart 表現を整列・貼り合わせることで,大域 latent 座標系を構成する.さらに,元座標空間,局所接空間,大域 latent の間に双方向の写像則を与えることにより,大域 latent 上で得られた候補解が元座標空間で復元可能となる.数値実験では,三次元ラプラシアン平滑化制約を事前情報として用いることでどの程度,解探索性能が向上するかを検証した.その結果,100次元及び300 次元という高次元空間に対しても,大域 latent 上でのヒューリスティック探索により,最適解に近い解を安定に探索できることを確認した.
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著者は,本研究に関連する特許を出願中である(発明の名称:Hit-and-Runと白色化座標変換による解探索空間の低次元化方法,出願番号:JP2026-065997,出願日:2026年3月24日)。ダウンロード *前日までの集計結果を表示します
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