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Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…
A structured version of derivative-free random pattern search optimization algorithms is introduced which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and…
Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…
Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we…
This paper is concerned with the strong approximation of a semi-linear stochastic wave equation with strong damping, driven by additive noise. Based on a spatial discretization performed by a spectral Galerkin method, we introduce a kind of…
We introduce a predictor-corrector discretisation scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1.0. The key feature of the new scheme is that it builds up…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive $e^+e^-$ annihilation (SIA) processes and setup a framework to sum them up to all orders…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor…
We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge…
We propose a linearly implicit structure-preserving numerical method for semilinear Hamiltonian systems with polynomial nonlinearities, combining Kahan's method and exponential integrator. This approach efficiently balances computational…
Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
Decoding in a Transformer based language model is inherently sequential as a token's embedding needs to pass through all the layers in the network before the generation of the next token can begin. In this work, we propose a new…
Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic $C^\ast$-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called…