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The study of vortex dynamics using a variational formulation has an extensive history and a rich literature. The standard Hamiltonian function that describes the dynamics of interacting point vortices of constant strength is the…
In molecular dynamics (MD) simulations, transitions between states are often rare events due to energy barriers that exceed the thermal temperature. Because of their infrequent occurrence and the huge number of degrees of freedom in…
Efficient exploration remains a challenging problem in reinforcement learning, especially for tasks where extrinsic rewards from environments are sparse or even totally disregarded. Significant advances based on intrinsic motivation show…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
A popular way to accelerate the sampling of rare events in molecular dynamics simulations is to introduce a potential that increases the fluctuations of selected collective variables. For this strategy to be successful, it is critical to…
Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed…
Sampling the free energy surface, namely, the distribution of collective variables (CVs), is a crucial problem in statistical physics, as it underpins a better understanding of chemical reactions and conformational transitions. Traditional…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
With an increasing high penetration of solar photovoltaic generation in electric power grids, voltage phasors and branch power flows experience more severe fluctuations. In this context, probabilistic power flow (PPF) study aims at…
Molecular generation conditioned on textual descriptions is a fundamental task in computational chemistry and drug discovery. Existing methods often struggle to simultaneously ensure high-quality, diverse generation and fast inference. In…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…
One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…