Related papers: Multilevel Summation for Dispersion: A Linear-Time…

To address the computational challenges of ab initio molecular dynamics and the accuracy limitations of empirical force fields, the introduction of machine learning force fields has proven effective in various systems including metals and…

The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical)…

Large language models (LLMs) have achieved remarkable success across various artificial intelligence tasks. However, their enormous sizes and computational demands pose significant challenges for the deployment on edge devices. To address…

We study the weak convergence behaviour of the Leimkuhler--Matthews method, a non-Markovian Euler-type scheme with the same computational cost as the Euler scheme, for the approximation of the stationary distribution of a one-dimensional…

Achieving distributed reinforcement learning (RL) for large-scale cooperative multi-agent systems (MASs) is challenging because: (i) each agent has access to only limited information; (ii) issues on convergence or computational complexity…

This article proposes a methodology to model and simulate complex systems, based on IRM4MLS, a generic agent-based meta-model able to deal with multi-level systems. This methodology permits the engineering of dynamic multi-level agent-based…

Typical biomolecular systems such as cellular membranes, DNA, and protein complexes are highly charged. Thus, efficient and accurate treatment of electrostatic interactions is of great importance in computational modelling of such systems.…

Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…

Multi-Agent Reinforcement Learning (MARL) discovers policies that maximize reward but do not have safety guarantees during the learning and deployment phases. Although shielding with Linear Temporal Logic (LTL) is a promising formal method…

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…

We introduce the Multilevel Euler-Maruyama (ML-EM) method compute solutions of SDEs and ODEs using a range of approximators $f^1,\dots,f^k$ to the drift $f$ with increasing accuracy and computational cost, only requiring a few evaluations…

Periodic or quasi-periodic phenomena reveal intrinsic characteristics in various natural processes, such as weather patterns, movement behaviors, traffic flows, and biological signals. Given that these phenomena span multiple modalities,…

Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space.…

We develop an accurate, highly efficient and scalable random batch sum-of-Gaussians (RBSOG) method for molecular dynamics simulations of systems with long-range interactions. The idea of the RBSOG method is based on a sum-of-Gaussians…

Recent research works on distributed adaptive networks have intensively studied the case where the nodes estimate a common parameter vector collaboratively. However, there are many applications that are multitask-oriented in the sense that…

Long-term time-series forecasting is essential for planning and decision-making in economics, energy, and transportation, where long foresight is required. To obtain such long foresight, models must be both efficient and effective in…

Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

We present the Linear Complexity Sequence Model (LCSM), a comprehensive solution that unites various sequence modeling techniques with linear complexity, including linear attention, state space model, long convolution, and linear RNN,…