Laurent El Ghaoui

The discovery of crystalline reticular materials remains largely trial-and-error despite their societal importance. We introduce our algorithmic iterative reticular synthesis (AIRES) cycle, which integrates automated synthesis, image recognition, single-crystal X-ray diffraction and, crucially, customized algorithmic decision-making, to maximize distinct crystal discoveries rather than optimizing single targets. Demonstrated on zeolitic imidazolate frameworks (ZIFs), AIRES achieves twice the discovery rate of random exploration, crystallizing 10 new linkers into diverse ZIF topologies and expanding the single-linker Zn-ZIF library by one-third. By transforming reticular synthesis from an empirical process to a systematic exploration, AIRES provides a scalable and efficient blueprint for accelerating materials discovery.

As the global focus on combating environmental pollution intensifies, the transition to sustainable energy sources, particularly in the form of electric vehicles (EVs), has become paramount. This paper addresses the pressing need for Smart Charging for EVs by developing a comprehensive mathematical model aimed at optimizing charging station management. The model aims to efficiently allocate the power from charging sockets to EVs, prioritizing cost minimization and avoiding energy waste. Computational simulations demonstrate the efficacy of the mathematical optimization model, which can unleash its full potential when the number of EVs at the charging station is high.

In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer depth and incorporation of feedback within their computational graph, are put to the test across various extrapolation scenarios: out-of-distribution, geographical, and temporal shifts. Our experiments consistently demonstrate significant performance advantage with implicit models. Unlike their non-implicit counterparts, which often rely on meticulous architectural design for each task, implicit models demonstrate the ability to learn complex model structures without the need for task-specific design, highlighting their robustness in handling unseen data.

We introduce a family of cardinality's lower bounds, defined as ratios of norms. We prove that the tightest bound of the family is obtained as a limit case, and involves a Shannon entropy. We then use this entropic lower bound in sparse optimization problems to approximate cardinality requirements. This provides a nonlinear nonconvex relaxed problem, which can be efficiently solved by off-the-shelf nonlinear solvers. In the numerical study, we focus on the case where the optimization is performed on the simplex, and where the classical l1 penalization does not yield sparse solution. The Finance Index Tracking problem is taken as an example and illustrates the efficiency of the proposed approach.

We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an empirical inverse Christoffel function: empirical inverse Christoffel functions are known to provide good approximations to the support of probability distributions. In addition to reachability analysis, the same approach can be applied to general problems of estimating the support of a random variable, which has applications in data science towards detection of novelties and outliers in data sets. In applications where safety is a concern, having a guarantee of accuracy that holds on finite data sets is critical. In this paper, we prove such bounds for our algorithms under the Probably Approximately Correct (PAC) framework. In addition to applying classical Vapnik- Chervonenkis (VC) dimension bound arguments, we apply the PAC-Bayes theorem by leveraging a formal connection between kernelized empirical inverse Christoffel functions and Gaussian process regression models.

We show that sparsity-constrained optimization problems over low-dimensional spaces tend to have a small duality gap. We use the Shapley--Folkman theorem to derive both data-driven bounds on the duality gap and an efficient primalization procedure to recover feasible points satisfying these bounds. These error bounds are proportional to the rate of growth of the objective with the target cardinality, which means in particular that the relaxation is nearly tight as soon as the target cardinality is large enough so that only uninformative features are added.

Estimation of topology of the power grid from electrical markets has been a point of interest of the industry traders. Under a DC model, methods [1], [2] try to recover the grid Laplacian though locational marginal prices (LMPs) exist. However they give incompatible grid Laplacian after the full recovery, leaving positive off diagonal entries. This paper discusses a new model for grid topology estimation, which involves the key property of diagonal dominance to guarantee a compatible full recovery of grid topology. We develop alternating direction method of multipliers (ADMM) algorithm for the new model which is much more scalable than existing algorithms aiming to solve the same problem thanks to the newly introduced sum-log-diagonal term. Numerical experiments indicate that our method is highly scalable to the number of nodes and/or to the number of time steps of the data while giving higher quality solution.