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Propagation and stability of stress-affected transformation fronts in solids

Sunday September 21th 2025 at 14:00 

Wolfson Building of Mechanical Engineering, Room 206

Abstract:

There is a wide range of problems in continuum mechanics that involve transformation fronts, which are non-stationary interfaces between two different phases in a phase-transforming or a chemically-transforming material. From the mathematical point of view, the considered problems are represented by systems of non-linear PDEs with discontinuities across non-stationary interfaces, kinetics of which depend on the solution of the PDEs. Such problems have a significant industrial relevance – an example of a transformation front is the localised stress-affected chemical reaction in Li-ion batteries with Si-based anodes. Since the kinetics of the transformation fronts depends on the continuum fields, the transformation front propagation can be decelerated and even blocked by the mechanical stresses. This talk will focus on three topics: (1) the stability of the transformation fronts in the vicinity of the equilibrium position for the chemo-mechanical problem, (2) a fictitious-domain finite-element method (CutFEM) for solving non-linear PDEs with transformation fronts and (3) an applied problem of Si lithiation.

Bio:

Mikhail Poluektov is currently appointed as a Lecturer in Mathematics at the University of Dundee (UK). His research focuses on computational and applied mathematics covering a large range of models and methods. In particular, his recent research includes fictitious-domain and multiscale methods for non-linear partial differential equations, as well as approximation theory methods. His work has been published in journals such as Computer Methods in Applied Mechanics and Engineering. Prior to current appointment, Dr Poluektov held a Senior Research Fellow position at the University of Warwick (UK). Dr Poluektov obtained a PhD from the Eindhoven University of Technology (Netherlands).

https://tau-ac-il.zoom.us/j/84875921874

Electrical Engineering Systems Seminar

Speaker: Maayan Shalom

M.Sc. student under the supervision of Dr. Alon Cohen

Monday, 2^nd July 2025, at 16:00

Generalization in Reinforcement Learning via Structural Priors

Abstract

Generalization is a central challenge in reinforcement learning (RL) applications where an agent must succeed across many possible environments, not merely the handful it encountered during training. We formalize this challenge by assuming that, before each episode, Nature draws an unknown Markov Decision Process (MDP) from a fixed—yet hidden—distribution, and the agent must learn, from a finite training sample of such MDPs, a policy whose expected return over the entire distribution is near-optimal.

Earlier theory has shown that this problem is intractable in the worst case: partial observability of the true MDP identity induces an Epistemic Partially Observable MDP (Epistemic-POMDP), whose sample complexity can grow exponentially with the planning horizon. While positive results do exist, they typically rely on regularized learning objectives or strong Bayesian priors.

In this thesis, we revisit generalization through two natural structural lenses that make the problem tractable without resorting to explicit regularization. The first is a uniform similarity assumption, where every pair of MDPs induces statistically similar trajectory distributions under any policy. In this setting, we show that plain Empirical Risk Minimization (ERM) achieves a generalization error of O(1/m), where m is the number of training environments. This improves over the best known O(1/4m) rate for regularized ERM and highlights how trajectory-level similarity implicitly curbs hypothesis-class complexity. The second is a decodability assumption, where a short trajectory prefix uniquely reveals the identity of the underlying MDP. We show that in this case, ERM again enjoys the same O(1/m) sample complexity. Our analysis constructs truncated policies that depend on history only until the MDP is identified, and then act optimally according to the identified model.

Together, these results provide new foundations for learning under epistemic uncertainty. They delineate precise conditions under which simple empirical learning suffices, quantify the role of environment structure in determining sample complexity, and offer guidance for the design of agents that must generalize reliably in practice.

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