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Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical…
The Direct Simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity \emph{ab initio}…
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the…
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some…
Identifying low-energy adsorption geometries on catalytic surfaces is a practical bottleneck for computational heterogeneous catalysis: the difficulty lies not only in the cost of density functional theory (DFT) but in proposing initial…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
We study a system of perfect integrate-and-fire inhibitory neurons. It is a system of stochastic processes which interact through receiving an instantaneous increase at the moments they reach certain thresholds. In the absence of…
Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…
This article presents a composite nonlinear feedback (CNF) control method using self-triggered (ST) adaptive dynamic programming (ADP) algorithm in a human-machine shared steering framework. For the overall system dynamics, a…
Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…
Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself,…
Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself,…
Reinforcement Learning (RL) has recently emerged as a powerful technique for improving image and video generation in Diffusion and Flow Matching models, specifically for enhancing output quality and alignment with prompts. A critical step…
We propose a very accurate computational scheme for the dynamics of a classical oscillator coupled to a molecular junction driven by a finite bias, including the finite mass effect. We focus on two minimal models for the molecular junction:…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular…
Formant tracking is investigated in this study by using trackers based on dynamic programming (DP) and deep neural nets (DNNs). Using the DP approach, six formant estimation methods were first compared. The six methods include linear…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
A popular branch of stochastic network calculus (SNC) utilizes moment-generating functions (MGFs) to characterize arrivals and services, which enables end-to-end performance analysis. However, existing traffic models for SNC cannot…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…