MS025 - Mathematical Aspects of Machine Learning Methods in Computional Mechanics
Keywords: approximation properties, error analysis, foundations of machine learning, neural operators, scientific machine learning, training, uncertainty quantification
Methods based on machine learning (ML) approaches are rapidly becoming a key technology in computational mechanics. For instance:
1. Neural networks may infer solutions to complex differential equations rapidly.
2. Different ML approaches may process and compress data from measurements and observations.
3. ML algorithms can learn various nonlinear phenomena and nonlinear reduced-order modeling approaches from data.
Despite the rapid algorithmic development, the basic mathematical principles underpinning ML methods' success still need to be well established, and much work remains to be done.
In this mini-symposium, we focus on mathematical aspects that can provide a better understanding of the properties of ML methods in computational mechanics in a broad sense. Topics of interest include but are not limited to approximation and generalization properties, convergence and stability properties, a posteriori error estimation, improved non-convex optimization methods, and analysis of training techniques and regularisation.
1. Neural networks may infer solutions to complex differential equations rapidly.
2. Different ML approaches may process and compress data from measurements and observations.
3. ML algorithms can learn various nonlinear phenomena and nonlinear reduced-order modeling approaches from data.
Despite the rapid algorithmic development, the basic mathematical principles underpinning ML methods' success still need to be well established, and much work remains to be done.
In this mini-symposium, we focus on mathematical aspects that can provide a better understanding of the properties of ML methods in computational mechanics in a broad sense. Topics of interest include but are not limited to approximation and generalization properties, convergence and stability properties, a posteriori error estimation, improved non-convex optimization methods, and analysis of training techniques and regularisation.
