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DTSTART:20070311T020000
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BEGIN:VEVENT
DTSTAMP:20230801T235442
DTSTART;TZID=America/Detroit:20231004T160000
DTEND;TZID=America/Detroit:20231004T170000
SUMMARY:Workshop / Seminar:Extreme Value Theory for particle systems with mean-field drift interaction.
DESCRIPTION:We establish an Extreme Value Theory for a class of systems of diffusive particles with mean-field interaction in the drifts. First\, we show that as the number of particles grows large\, a point process that captures the upper order statistics of the system has the same limit as when the particles are replaced by independent copies of solution to the corresponding McKean-Vlasov SDE (propagation of chaos). Then\, we employ tools from standard Extreme Value Theory along with Malliavin Calculus to characterize the limit. We deduce that under certain growth conditions\, the normalized top-ranked particle will acquire a Gumbel law in the large-population limit.
UID:109658-21822569@events.umich.edu
URL:https://events.umich.edu/event/109658
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230918T104220
DTSTART;TZID=America/Detroit:20231011T160000
DTEND;TZID=America/Detroit:20231011T170000
SUMMARY:Workshop / Seminar:Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space
DESCRIPTION:We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions that are Lipschitz continuous in the measure in a Fourier-Wasserstein metric and uniformly continuous in time. The class of equations we consider is motivated by Mckean-Vlasov control problems with common noise and filtering problems. The proof of comparison relies on a novel version of Ishii's lemma\, which is tailor-made for the class of equations we consider.\n\nJoint work with Erhan Bayraktar and Xin Zhang.
UID:110951-21825898@events.umich.edu
URL:https://events.umich.edu/event/110951
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230905T090240
DTSTART;TZID=America/Detroit:20231018T160000
DTEND;TZID=America/Detroit:20231018T170000
SUMMARY:Workshop / Seminar:Asymptotic Analysis of Deep Residual Networks and Convergence of Gradient Descent Methods
DESCRIPTION:Residual networks (ResNets) have displayed impressive results in pattern recognition and\, recently\, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture\, such as the smoothness of the activation function\, we prove the existence of an alternative ODE limit\, a stochastic differential equation\, or neither of these. For each case\, we also derive the limit of the backpropagation dynamics and address its adaptiveness issue. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.\n \nWhen the gradient descent method is applied to the training of ResNets\, we prove that it converges linearly to a global minimum if the network is sufficiently deep and the initialization is sufficiently small. In addition\, the global minimum found by the gradient descent method has finite quadratic variation without using any regularization in the training. This confirms existing empirical results that the gradient descent method enjoys an implicit regularization property and is capable of generalizing to unseen data.\n \nThis is based on joint work with Rama Cont (Oxford)\, Alain Rossier (Oxford)\, and Alain-Sam Cohen (InstaDeep).
UID:110144-21824397@events.umich.edu
URL:https://events.umich.edu/event/110144
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230918T104255
DTSTART;TZID=America/Detroit:20231025T160000
DTEND;TZID=America/Detroit:20231025T170000
SUMMARY:Workshop / Seminar:Multistage distributionally robust optimization with adapted Wasserstein distance
DESCRIPTION:In this talk\, we will discuss multistage distributionally robust optimization in which the uncertainty set of stochastic processes is defined through the adapted Wasserstein distance. First\, I will present a dynamic programming reformulation to evaluate the worst-case risk of a given stochastic process and discuss the issue of time consistency. Second\, in the context of linear and stagewise-independent setting\, I will present a class of decision rules\, termed \"best-neighbor\" policy\, that are provably robust optimal.
UID:110268-21824695@events.umich.edu
URL:https://events.umich.edu/event/110268
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230922T155056
DTSTART;TZID=America/Detroit:20231115T160000
DTEND;TZID=America/Detroit:20231115T170000
SUMMARY:Workshop / Seminar:Van Eenam Seminar II: Computing Free Boundaries by Neural Networks and Simulations
DESCRIPTION:Abstract: This talk discusses a numerical method for the computation of free boundaries when a stochastic representation is available. It is based on an algorithm which we call deep empirical risk minimization developed by E\, Han & Jentzen. Their approach applies generally to many stochastic optimal control problems. In the presence of free boundaries\, it has to be modified to account for training based on hitting times. In this talk\, I outline how this is achieved for the classical problems of optimal stopping or the obstacle problem\, and for the Stefan problem for the water-ice interfaces. For the Stefan problem\, we use the recent stochastic representations\, the notion of physical probabilistic solutions\, and level-sets parameterized by deep neural networks on the numerical side.
UID:109661-21822571@events.umich.edu
URL:https://events.umich.edu/event/109661
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:AEM Featured,Mathematics
LOCATION:East Hall - 1360
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20230922T155111
DTSTART;TZID=America/Detroit:20231116T170000
DTEND;TZID=America/Detroit:20231116T180000
SUMMARY:Workshop / Seminar:Van Eenam Seminar III: Eikonal Equations on Wasserstein Spaces
DESCRIPTION:Abstract: Mean-field or McKean-Vlasov type optimal control is closely related to the exciting program of mean-field games. Dynamic programming approach to these control problems result in nonlinear partial differential equations on the space of probability measures. These equations not only require the solution to be differentiable but impose further regularity on the derivatives which are being on the dual of the set of measures are also functions themselves. Despite these difficulties\, several approaches to characterize the value function of the control problems as the unique appropriate weak solutions have been developed. In this talk\, I discuss a comparison result between sup and super viscosity solutions of the associated dynamic programing equations. Main technical result uses negative Sobolev norms and the classical techniques from the viscosity theory.
UID:109662-21822572@events.umich.edu
URL:https://events.umich.edu/event/109662
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:AEM Featured,Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230918T104409
DTSTART;TZID=America/Detroit:20240221T160000
DTEND;TZID=America/Detroit:20240221T170000
SUMMARY:Workshop / Seminar:TBA
DESCRIPTION:TBA
UID:110937-21825884@events.umich.edu
URL:https://events.umich.edu/event/110937
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230918T104351
DTSTART;TZID=America/Detroit:20240320T160000
DTEND;TZID=America/Detroit:20240320T170000
SUMMARY:Workshop / Seminar:TBA
DESCRIPTION:TBA
UID:110936-21825883@events.umich.edu
URL:https://events.umich.edu/event/110936
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230918T104424
DTSTART;TZID=America/Detroit:20240403T160000
DTEND;TZID=America/Detroit:20240403T170000
SUMMARY:Workshop / Seminar:Mean-Field Games for Scalable Computation and Diverse Applications
DESCRIPTION:Mean field games (MFGs) study strategic decision-making in large populations where individual players interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example\, the Nash equilibrium of MFGs forms a pair of PDEs\, which connects and extends variational optimal transport problems. This talk will present recent progress in this direction\, focusing on computational MFG and engineering applications in robotics path planning\, pandemics control\, and Bayesian/AI sampling algorithms. This is based on joint work with the MURI team led by Stanley Osher (UCLA).
UID:111486-21827175@events.umich.edu
URL:https://events.umich.edu/event/111486
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230918T104522
DTSTART;TZID=America/Detroit:20240417T160000
DTEND;TZID=America/Detroit:20240417T170000
SUMMARY:Workshop / Seminar:TBA
DESCRIPTION:TBA
UID:112183-21828569@events.umich.edu
URL:https://events.umich.edu/event/112183
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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