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SUMMARY:Neural Wave Functions for the Electronic Schrödinger Equation: A 
 Mathematical Case Study in Scientific Computing.
DTSTART:20260518T104500Z
DTEND:20260518T120000Z
DTSTAMP:20260518T072100Z
UID:indico-event-1331@math-events.uni-bonn.de
CONTACT:karabash@lam.uni-bonn.de
DESCRIPTION:Speakers: Philipp Grohs (Universität Wien)\n\nDeep learning h
 as attracted considerable attention in scientific computing\, from neural-
 network ansätze for partial differential equations to data-driven surroga
 te 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 perspect
 ive on this phenomenon\, including complexity-theoretic upper and lower bo
 unds that clarify both the limitations of deep-learning-based methods and 
 the special structures under which they can succeed.The electronic Schröd
 inger equation provides a particularly compelling example of such a succes
 s. In computational quantum chemistry\, deep-learning variational Monte Ca
 rlo (VMC) has led to striking empirical progress through highly expressive
  neural-network wave functions. At the same time\, this success raises del
 icate mathematical questions. I will discuss recent results showing that t
 he nodal geometry of the wave function governs the integrability of the lo
 cal energy and of VMC gradient estimators\, leading naturally to heavy-tai
 led stochastic optimization problems. Motivated by this analysis\, I will 
 present a clipped VMC optimization algorithm and prove its convergence und
 er precisely the weak-moment assumptions identified by the nodal theory. T
 he talk will conclude with open questions at the interface of approximatio
 n theory\, probability\, optimization\, and computational quantum chemistr
 y.\n\nhttps://math-events.uni-bonn.de/event/1331/
LOCATION:Seminar Room 1.008 (Endenicher Allee 60)
URL:https://math-events.uni-bonn.de/event/1331/
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