Alexander Effland and I, jointly with Anton Bovier and Christian Brennecke, are organizing the Oberseminar “Mathematics of Artificial Intelligence” (Math-of-AI). 

The seminar takes place several times per semester on 

Mondays from 12:45 to 14:00 in the seminar room 1.008 (Endenicher Allee 60).

• 18.05.2026, at 12:45 in the seminar room 1.008 (Endenicher Allee 60).
  Philipp Grohs (Universität Wien)
  Title: Neural Wave Functions for the Electronic Schrödinger Equation: A Mathematical Case Study in Scientific Computing.
  Abstract.
  
   
• 20.07.2026, Veronique Gayrard (CNRS & Marseille Institute of Mathematics)
  Title: TBA
  Abstract: TBA

• tentatively 07.12.2026, Afonso S. Bandeira (ETH Zürich),
  Title: TBA
  Abstract: TBA
• tentatively January 2027, Lars Grüne (University of Bayreuth) 
  Title: TBA
  Abstract: TBA

18.05.2026, Philipp Grohs (Universität Wien) "Neural Wave Functions for the Electronic Schrödinger Equation: A Mathematical Case Study in Scientific Computing”

Abstract. Deep learning has attracted considerable attention in scientific computing, from neural-network ansätze for partial differential equations to data-driven surrogate models for complex first-principles simulations. Its impact, however, has been uneven: in many standard settings, classical numerical methods remain difficult to outperform. I will begin with a brief broader perspective on this phenomenon, including complexity-theoretic upper and lower bounds that clarify both the limitations of deep-learning-based methods and the special structures under which they can succeed.
The electronic Schrödinger equation provides a particularly compelling example of such a success. In computational quantum chemistry, deep-learning variational Monte Carlo (VMC) has led to striking empirical progress through highly expressive neural-network wave functions. At the same time, this success raises delicate mathematical questions. I will discuss recent results showing that the nodal geometry of the wave function governs the integrability of the local energy and of VMC gradient estimators, leading naturally to heavy-tailed stochastic optimization problems. Motivated by this analysis, I will present a clipped VMC optimization algorithm and prove its convergence under precisely the weak-moment assumptions identified by the nodal theory. The talk will conclude with open questions at the interface of approximation theory, probability, optimization, and computational quantum chemistry.