Martin Eigel

Martin Eigel is a Researcher at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), specializing in numerical methods for stochastic partial differential equations, uncertainty quantification, and machine learning applications in computational mathematics. His work bridges tensor networks, Bayesian inversion, and quantum simulations.

Research Interests:

• Adaptive stochastic Galerkin finite element methods
• Low-rank tensor approximations for high-dimensional problems
• Machine learning integration with PDE solvers
• Quantum circuit simulation techniques
• Bayesian inverse problems and error control

Key Article Trends: His recent publications focus on merging deep learning architectures (e.g., ResNet, CNNs) with stochastic and tensor-based numerical methods for solving parametric PDEs, Bayesian inversion, and quantum systems. Topics include Hamilton-Jacobi-Bellman equations, Langevin dynamics, and risk-averse optimization under uncertainty.