*일시 : 4월 15일(수), 16:30-
* 연사 : 이승규 교수(고려대학교 응용수리과학부)
* 장소 : 응용수학연습실(베어드홀 426호)
* 제목 : PDE-informed machine learning framework for structured and unstructured data classification
*초록
Phase-field models provide a well-structured variational framework for representing decision boundaries, offering a mathematically interpretable alternative to conventional machine-learning approaches. However, their practical use in data classification has been limited by the substantial computational cost of solving nonlinear parabolic PDEs. In this work, we present a PDE-based learning method for data classification by employing the Allen-Cahn equation with a fidelity term. To enable practical applicability, we introduce an efficient, matrix-free, and structure-preserving numerical strategy that ensures stability through the maximum principle while maintaining the computational advantages of explicit schemes. The resulting classifier produces robust class separation and demonstrates competitive performance across synthetic and real datasets, achieving accuracy comparable to SVMs and ANNs with significantly reduced computational cost. These findings indicate that phase-field models, combined with stability-preserving discretizations, offer a promising and interpretable alternative for modern classification tasks and can be extended to high-dimensional or graph-based data environments.