I will give a self-contained introduction to the theory of the neural network function class and its application to image classification and numerical solution of partial differential equations.

I will give a self-contained introduction to the theory of the neural network function class and its application to image classification and numerical solution of partial differential equations.

This talk is devoted to the study of a monetary model proposed by Rotemberg (Journal of Political Economy, 1984). Rotemberg’s model provided a general dynamic structure for investigating government intervention in the open market operation and it has inspired the development of many other models in related fields. This talk concerns a very basic theoretical question on the model, namely the existence and the uniqueness of the equilibrium, which has been an open problem since the publication of Rotemberg’s original paper. This question was partially addressed by Rotemberg by analyzing the linearization of the equation which governs the equilibrium and obtaining a numerical solution around the steady state equilibrium. 

I will give a self-contained introduction to the theory of the neural network function class and its application to image classification and numerical solution of partial differential equations.

We develop a data-driven methodology based on parametric Itô's Stochastic Differential Equations (SDEs) to capture forecast errors' asymmetric dynamics, including the forecast's uncertainty at time zero.

Despite the recent advances in big data processing, enabled by the emergence of large-scale machine learning techniques, several statistical questions regarding the behavior in the regime of high dimensions of well-established and fundamental methods have remained unresolved.

Often in the context of data centric science and engineering applications, one endeavours to learn complex systems in order to make more informed predictions and high stakes decisions under uncertainty. Some key challenges which must be met in this context are robustness, generalizability, and interpretability.

The talk will present our efforts to develop the next generation operational systems for the Red Sea and the Arabian Gulf, as part of Aramco’s resolution toward the Fourth Industrial Revolution. These integrated systems, we refer to as iReds and iGulf, have been built around state-of-the-art ocean-atmosphere-wave general circulation models that have been specifically developed for the region and nested within the global weather systems.

As a fundamental problem in both machine learning and privacy, Empirical Risk Minimization in the Differential Privacy Model (DP-ERM) received much attentions. However, most of the previous studies are either in the central DP model or interactive LDP model. In this talk, I will discuss some recent developments of DP-ERM in the non-interactive LDP model.

In this talk I report some results on the approximation of fluid-structure interaction problems using non matching grids. Our formulation originates from the Immersed Boundary Method and then moved toward the Fictitious Domain approach. The advantages of this formulation is that it avoids the difficulties related with mesh generation and it allows the treatment of fluid and solid in their natural Eulerian and Lagrangian framework. I present the well-posedness of our formulation at the continuous level in a simplified setting. Moreover, I shall discuss various time discretizations that provide unconditionally stable schemes and some computational details.

Modeling, estimation and prediction of spatial extremes is key for risk assessment in a wide range of geo-environmental, geo-physical, and climate science applications. In this work, we propose a flexible approach for modeling and estimating extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the whole Red Sea, a vital region of high biodiversity.

We consider statistical inference for a class of agent-based SIS and SIR models. In these models, agents infect one another according to random contacts made over a social network, with an infection rate that depends on individual attributes. Infected agents might recover according to another random mechanism that also depends on individual attributes, and observations might involve occasional noisy measurements of the number of infected agents. Likelihood-based inference for such models presents various computational challenges. In this talk, I will present various sequential Monte Carlo algorithms to address these challenges.

In this talk, I will describe three use cases that highlight present challenges and opportunities for the development of machine learning methodology for applications in healthcare. First, I will describe the development of simple word embedding approaches for bag of-documents classification and its applications to diagnosis of peripheral artery disease from clinical narratives. Second, I will present an approach for volumetric image classification that leverages attention mechanisms, contrastive learning and feature-encoding sharing for geographic atrophy prognosis from optical coherence tomography images. Third, I will discuss machine learning approaches for multi-modal and multi-dataset integration for biomarker discovery from molecular (omics) data. To conclude, I will summarize the contributions and insights in each of these different directions in which relatively low sample sizes are the common denominator.

Workshop's Agenda

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I will focus on the envelope formula, an essential tool and a unifying framework for the first-order analysis of value functions in parameter-dependent optimization problems. In particular, I will discuss formal differentiation rules of value functions and derive a few familiar examples as particular cases of this technique, such as the Hamilton-Jacobi-Bellman PDE and the adjoint method. I will then discuss how to turn these formal differentiation rules into rigorous theorems via perturbation analysis of optimization problems. Finally, I will apply these ideas to parameter identification problems based on optimal transportation distances and variational analysis of mean-field games.

I will focus on the envelope formula, an essential tool and a unifying framework for the first-order analysis of value functions in parameter-dependent optimization problems. In particular, I will discuss formal differentiation rules of value functions and derive a few familiar examples as particular cases of this technique, such as the Hamilton-Jacobi-Bellman PDE and the adjoint method. I will then discuss how to turn these formal differentiation rules into rigorous theorems via perturbation analysis of optimization problems. Finally, I will apply these ideas to parameter identification problems based on optimal transportation distances and variational analysis of mean-field games.

In this short course I will introduce some elements of bifurcation theory, such as the Lyapunov-Schmidt reduction, the bifurcation from the simple eigenvalue, and the Krasnoselski bifurcation theorem. Then, I will discuss some applications to the theory of MFG systems: existence of periodic in time solutions, and multi-population problems.

I will focus on the envelope formula, an essential tool and a unifying framework for the first-order analysis of value functions in parameter-dependent optimization problems. In particular, I will discuss formal differentiation rules of value functions and derive a few familiar examples as particular cases of this technique, such as the Hamilton-Jacobi-Bellman PDE and the adjoint method. I will then discuss how to turn these formal differentiation rules into rigorous theorems via perturbation analysis of optimization problems. Finally, I will apply these ideas to parameter identification problems based on optimal transportation distances and variational analysis of mean-field games.

In this short course I will introduce some elements of bifurcation theory, such as the Lyapunov-Schmidt reduction, the bifurcation from the simple eigenvalue, and the Krasnoselski bifurcation theorem. Then, I will discuss some applications to the theory of MFG systems: existence of periodic in time solutions, and multi-population problems.

We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim).

We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim).

Abstract

As simulation and analytics enter the exascale era, numerical algorithms must span a wide

We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim)

Explosive volcanic eruptions are magnificent events that in many ways affect the Earth’s natural processes and climate. They cause sporadic perturbations of the planet’s energy balance, activating complex climate feedbacks and providing unique opportunities to better quantify those processes. We know that explosive eruptions cause cooling in the atmosphere for a few years, but we have just recently realized that they affect the major climate variability modes and volcanic signals can be seen in the subsurface ocean for decades. The volcanic forcing of the previous two centuries offsets the ocean heat uptake and diminishes global warming by about 30%. In the future, explosive volcanism could slightly delay the pace of global warming and has to be accounted for in long-term climate predictions. The recent interest in dynamic, microphysical, chemical and climate impacts of volcanic eruptions is also excited by the fact these impacts provide a natural analog for climate geoengineering schemes involving the deliberate development of an artificial aerosol layer in the lower stratosphere to counteract global warming. In this talk, I will discuss these recently discovered volcanic effects and specifically pay attention to how we can learn about the hidden Earth-system mechanisms activated by explosive volcanic eruptions.

We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton's method from which it inherits its fast local quadratic rate. However, unlike Newton's method, NEWTON-STAR enjoys the same per iteration communication cost as gradient descent. While this method is impractical as it relies on the use of certain unknown parameters characterizing the Hessian of the objective function at the optimum, it serves as the starting point which enables us to design practical variants thereof with strong theoretical guarantees. In particular, we design a stochastic sparsification strategy for learning the unknown parameters in an iterative fashion in a communication efficient manner. Applying this strategy to NEWTON-STAR leads to our next method, NEWTON-LEARN, for which we prove local linear and superlinear rates independent of the condition number. When applicable, this method can have dramatically superior convergence behavior when compared to state-of-the-art methods. Finally, we develop a globalization strategy using cubic regularization which leads to our next method, CUBIC-NEWTON-LEARN, for which we prove global sublinear and linear convergence rates, and a fast superlinear rate. Our results are supported with experimental results on real datasets, and show several orders of magnitude improvement on baseline and state-of-the-art methods in terms of communication complexity.