HAL Paris Dauphine-PSL
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LLMs can Schedule
No full textInternational audienceThe job shop scheduling problem (JSSP) remains a significant hurdle inoptimizing production processes. This challenge involves efficiently allocating jobsto a limited number of machines while minimizing factors like total processing timeor job delays. While recent advancements in artificial intelligence have yieldedpromising solutions, such as reinforcement learning and graph neural networks,this paper explores the potential of Large Language Models (LLMs) for JSSP. Weintroduce the very first supervised 120k dataset specifically designed to train LLMsfor JSSP. Surprisingly, our findings demonstrate that LLM-based scheduling canachieve performance comparable to other neural approaches. Furthermore, wepropose a sampling method that enhances the effectiveness of LLMs in tacklingJSSP
Exploring Large Action Sets with Hyperspherical Embeddings using von Mises-Fisher Sampling.
No full textInternational audienc
Autour du problème de l’existence globale pour des systèmes de la mécanique des fluides visqueux avec ou sans capillarité
No full textThis thesis is devoted to the study of several systems modeling fluid mechanics phenomena, such as the flow of viscous fluids, compressible or incompressible ,with or without capillarity. In the first part, we revisit local-in-time existence results for solutions to partially diffusive hyperbolic systems. We establish such results for initial data in textit {critical regularity spaces}. We then prove the existence of global-in-time solutions for small initial data in critical homogeneous Besov spaces. Moreover, we justify the convergence, as time tends to infinity, toward stable stationary states, with an algebraic rate of convergence. The second part focuses on the global well-posedness of a compressible two-phase flow model involving a smooth phase transition. More precisely, we show that starting from large initial data in Lebesgue spaces, one can still construct global-in-time solutions within the same functional framework. Finally, the third part addresses the study of an incompressible multiphase fluid flow. While the existence and uniqueness of global-in-time solutions are well understood when the initial density is bounded, the problem becomes more delicate when this assumption is dropped. We show that if the initial density belongs to a Yudovich-type space, it is still possible to construct global-in-time solutions.Cette thèse est consacrée à l’étude de plusieurs systèmes modélisant des phénomènes de la mécanique des fluides, tels que l’écoulement de fluides visqueux, compressibles ou incompressibles, avec ou sans capillarité. Dans la première partie, nous revisitons les résultats d’existence locale en temps pour les solutions de systèmes hyperboliques partiellement diffusifs. Nous obtenons des résultats dans des espaces à régularité critique, pour des données initiales appropriées. Par la suite, nous établissons l’existence de solutions globales en temps pour de petites données initiales, dans des espaces de Besov homogènes critiques. Nous justifions également la convergence à temps grand vers des états stationnaires stables, avec un taux de convergence algébrique. La deuxième partie est dédiée à l’analyse du caractère bien posé global d’un écoulement compressible biphasique, incluant une transition de phase régulière. Plus précisément, nous montrons que, partant de données initiales grandes dans des espaces de Lebesgue, il est possible de construire des solutions globales en temps dans ces mêmes espaces. Enfin, la dernière partie porte sur l’étude d’un écoulement de fluide incompressible multiphasique. Si l’existence et l’unicité de solutions globales en temps sont bien comprises lorsque la densité initiale est bornée, la situation est moins comprise lorsque cette densité ne l’est pas. Nous démontrons que, si la densité initiale appartient à un espace de type Yudovich, il est néanmoins possible de construire des solutions globales en temps
Global derivation of a Boussinesq–Navier–Stokes type system from fluid-kinetic equations
No full textInternational audienceWe study a hydrodynamic limit of the Vlasov–Navier–Stokes system with external gravity force. We answer a question raised by Han-Kwan and Michel in [48] concerning the limit towards a Boussinesq–Navier–Stokes type system. Our work provides a rigorous derivation of such hydrodynamic equations for arbitrarily large times, starting from the previous fluid-kinetic coupling. To do so, we consider a particular spatial geometric setting corresponding to the half-space case. Our proof is based on an absorption effect at the boundary which leads to crucial decay in time estimates
Bayesian Hierarchical Finite Mixture Models of Reading Times: A Case Study
No full textWe present a case study demonstrating the importance of Bayesian hierarchical mixture models as a modelling tool for evaluating the predictions of competing theories of cognitive processes. As a case study, we revisit two published data sets from psycholinguistics. In sentence comprehension, it is widely assumed that the distance between linguistic co-dependents affects the latency of dependency resolution: the longer the distance, the longer the time taken to complete the dependency (e.g., Gibson 2000). An alternative theory, direct access (McElree, 1993), assumes that retrieval times are a mixture of two distributions (Nicenboim & Vasishth, 2017): one distribution represents successful retrievals and the other represents an initial failure to retrieve the correct dependent, followed by a reanalysis that leads to successful retrieval. Here, dependency distance has the effect that in long-distance conditions the proportion of reanalyses is higher. We implement both theories as Bayesian hierarchical models and show that the direct-access model fits the Chinese relative clause reading time data better than the dependency-distance account. This work makes several novel contributions. First, we demonstrate how the researcher can reason about the underlying generative process of their data, thereby expressing the underlying cognitive process as a statistical model. Second, we show how models that have been developed in an exploratory manner to represent different underlying generative processes can be compared in terms of their predictive performance, using both K-fold cross validation on existing data, and using completely new data. Finally, we show how the models can be evaluated using simulated data
Regenerating desires at the eve of a war: the rise of digital capitalism
No full textInternational audienceKeynote lecture delivered at the Mediterrean Conference on Information Systems (MCIS) in Nantes. Presentation of my book The Rise of Digital Management: From Industrial Mobilization to Platform Capitalism (Routledge)
A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem
No full textInternational audienceIn the first part of this paper, we derive an infinite dimensional partial differential equation which describes an economic equilibrium in a model of storage which includes an infinite number of non-atomic agents. This equation has the form of a mean field game master equation. The second part of the paper is devoted to the mathematical study of the Hamilton-Jacobi-Bellman equation from which the previous equation derives. This last equation is both singular and set on a Hilbert space and thus raises new mathematical difficulties