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Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel…
Forecasting is critical in areas such as finance, biology, and healthcare. Despite the progress in the field, making accurate forecasts remains challenging because real-world time series contain both global trends, local fine-grained…
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…
The recent advancement of foundation models (FMs) has brought about a paradigm shift, revolutionizing various sectors worldwide. The popular optimizers used to train these models are stochastic gradient descent-based algorithms, which face…
Accurately forecasting GPU workloads is essential for AI infrastructure, enabling efficient scheduling, resource allocation, and power management. Modern workloads are highly volatile, multiple periodicity, and heterogeneous, making them…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…
Comparing post-training LLM variants, such as quantized, LoRA-adapted, and distilled models, requires a diagnostic that identifies how a variant has drifted, not only whether it has degraded. Existing similarity scores such as CKA and SVCCA…
Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of…
This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…
Simulation plays a central role in scientific discovery. In many applications, the bottleneck is no longer running a simulator; it is choosing among large families of plausible simulators, each corresponding to different forward…
Accurate long-range prediction of geophysical systems is difficult due to strongly nonlinear dynamics, the high computational cost of full-physics simulations, and the error accumulation that arise when one-step autoregressive surrogates…
This work studies heterogeneous Multi-Objective Reinforcement Learning (MORL), where objectives can differ sharply in temporal frequency. Such heterogeneity allows dense objectives to dominate learning, while sparse long-horizon rewards…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
Learning complex multi-agent system dynamics from data is crucial across many domains, such as in physical simulations and material modeling. Extended from purely data-driven approaches, existing physics-informed approaches such as…
Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on…
While Hybrid Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) has become the standard paradigm for training LLM agents, effective mechanisms for data allocation between these stages remain largely underexplored. Current…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type H\"ormander condition, assuming H\"older regularity assumptions on the drift coefficient.…