The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard approaches typically require high-fidelity training data. In many practical settings, the data are indirectly observed through noisy and nonlinear measurement. The challenge lies not only in approximating the coefficients of the SDEs, but in simultaneously inferring the posterior updates given the observations. In this work, we present a neural path estimation approach to solve stochastic dynamical systems based on variational inference. We first derive a stochastic control problem that solve filtering posterior path measure corresponding to a pathwise Zakai equation. We then construct a generative model that maps the prior path measure to posterior measure through the controlled diffusion and the associated Randon-Nykodym derivative. Through an amortization of sample paths of the observation process, the control is learned by an embedding of the noisy observation paths. Thus, we learn the unknown prior SDE and the control can recover the conditional path measure given the observation sample paths and we learn an associated SDE which induces the same path measure. In the end, we perform experiments on nonlinear dynamical systems, demonstrating the model's ability to learn multimodal, chaotic, or high dimensional systems.

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys methodological and theoretical developments at the intersection of operator learning and inverse problems. It begins by summarizing the probabilistic and deterministic approaches to inverse problems, and pays special attention to emerging measure-centric formulations that treat observed data or unknown parameters as probability distributions. The discussion then turns to operator learning by covering essential components such as data generation, loss functions, and widely used architectures for representing function-to-function maps. The core of the chapter centers on the end-to-end inverse operator learning paradigm, which aims to directly map observed data to the solution of the inverse problem without requiring explicit knowledge of the forward map. It highlights the unique challenge that noise plays in this data-driven inversion setting, presents structure-aware architectures for both point predictions and posterior estimates, and surveys relevant theory for linear and nonlinear inverse problems. The chapter also discusses the estimation of priors and regularizers, where operator learning is used more selectively within classical inversion algorithms.

Due to rising demands for Artificial Inteligence (AI) inference, especially in higher education, novel solutions utilising existing infrastructure are emerging. The utilisation of High-Performance Computing (HPC) has become a prevalent approach for the implementation of such solutions. However, the classical operating model of HPC does not adapt well to the requirements of synchronous, user-facing dynamic AI application workloads. In this paper, we propose our solution that serves LLMs by integrating vLLM, Slurm and Kubernetes on the supercomputer \textit{RAMSES}. The initial benchmark indicates that the proposed architecture scales efficiently for 100, 500 and 1000 concurrent requests, incurring only an overhead of approximately 500 ms in terms of end-to-end latency.

By definition, its roots (those t where p( t) = 0) are the eigenvalues of A . Furthermore, the SISO LDS are almost surely reachable, and share the same canonical form matrix. Now we verify that the SISO LDS are almost surely reachable, assuming the MISO LDS is reachable. We briefly review their method, showing how it gives rise to a multiplicative variant of LDStack. We begin by viewing the RNN as an Euler discretization of a continuous-time dynamical system (e.g. The SDC factorization can be derived in a straightforward manner.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations.

As discussed in the main text, there could be many ways to incorporate anatomical priors into our formulation. Here, we demonstrate one example--assuming that brain regions are sparsely connected, and therefore many blocks of the dynamics matrices will be zero. This can be implemented using a block-wise spike-and-slab prior on the dynamics matrices. A.1 Formulation We want a block-sparse prior for dynamics matrices. We break down this matrix into a B B set of blocks, where B is the number of neural populations.

Y et, in most cases, a suitably adjusted version of Lloyd's algorithm --