hybrid dynamics sampling

This work addresses the challenge of efficiently sampling from Gibbs distributions in complex energy landscapes characterized by barriers or metastable states. The authors propose a hybrid stochastic dynamics framework that employs two distinct sampling dynamics in different regions of the state space, coupled at their interface through a natural transmission condition that preserves the target distribution. By introducing a regularization mechanism, they establish—for the first time—the exponential convergence rate of this hybrid dynamics. In radially symmetric potentials, the method significantly reduces the mean escape time compared to conventional approaches. Both theoretical analysis and numerical experiments demonstrate that the proposed scheme offers marked improvements over traditional sampling strategies in terms of convergence speed and the ability to overcome metastability.

Molecular dynamics simulations in high-dimensional energy landscapes suffer from limited phase-space sampling due to physical constraints and energetic barriers, hindering accurate reconstruction of high-fidelity free energy surfaces (FES). Method: We propose a consensus-driven min–max adaptive surrogate modeling framework that jointly optimizes surrogate approximation and residual-guided adaptive sampling. It integrates Laplacian-residual peak localization with a temperature-controlled stochastic interacting particle system, enabling closed-loop optimization of phase-space exploration and FES reconstruction under physical constraints. Contribution/Results: This work is the first to introduce min–max optimization into FES construction, achieving coupled sampling–modeling updates driven by residual error. Validated on biomolecular systems with up to 30 collective variables, it significantly improves sampling efficiency and surrogate generalizability, achieving state-of-the-art FES accuracy.

Sampling transition pathways between metastable molecular states under high energy barriers remains challenging: conventional molecular dynamics simulations suffer from low efficiency, while AI-based methods relying on hand-crafted collective variables exhibit poor generalizability. To address this, we propose the unbiased and scalable Diffusion Path Sampler (DPS). Our key contributions are: (1) the first learnable control variate framework based on log-variance divergence, integrated with an off-policy reinforcement learning scheme; (2) synergistic incorporation of a replay buffer and simulated annealing to enhance sample efficiency and pathway diversity; and (3) scale-equivariant biased force parameterization, enabling robust modeling of large-scale systems. Evaluated on synthetic potentials, small peptides, and fast-folding proteins, DPS consistently outperforms baselines—generating physically realistic, diverse, and generalizable transition pathways with significantly improved sampling efficiency.

Discrete-state-space generative models—e.g., for small molecules, DNA, and protein sequences—lack principled, controllable guidance mechanisms. Existing continuous-domain guidance paradigms do not generalize to discrete spaces, hindering attribute-controlled generation. Method: This paper introduces the first general, differentiable guidance framework for discrete generative models based on continuous-time Markov processes, unifying discrete diffusion and flow-matching architectures. It overcomes the fundamental incompatibility of continuous guidance with discrete state spaces by establishing a theoretically grounded guidance theory for discrete domains. The framework enables arbitrary differentiable guidance objectives without model retraining, leveraging probability path reweighting and gradient-driven discrete sampling. Contribution/Results: Experiments demonstrate substantial improvements in target property satisfaction rates and sample diversity across diverse biomolecular generation tasks, while maintaining flexibility and strong generalization across guidance objectives and model architectures.

Standard MCMC methods for Bayesian parameter estimation in ODEs suffer from high rejection rates, slow convergence, and excessive computational cost due to strong nonlinear dependencies among parameters and states. To address this, we propose a constraint-satisfying Langevin dynamics method that directly samples on the joint state-parameter manifold, embedding the ODE dynamics as hard constraints into the sampling process—thereby eliminating repeated forward numerical integration. Our approach uniquely integrates Langevin dynamics, trajectory optimization, and numerical continuation techniques within a constrained differential equation framework, enabling efficient posterior sampling while rigorously preserving the structural integrity of ODE solutions. Evaluated on a biochemical oscillator model, the method achieves over 100× improvement in sampling efficiency compared to standard MCMC. It accurately resolves Hopf bifurcations and characterizes limit-cycle regions, significantly enhancing uncertainty quantification and model selection capabilities.

Molecular dynamics simulations are inherently serial, making it challenging to improve single-system throughput via parallel computation. This work proposes Langevin Speculative Dynamics (LSD), the first method to extend speculative sampling to second-order Langevin dynamics. LSD introduces a model-agnostic, distributed speculation mechanism that leverages a fast draft model to propose steps, which are then validated in parallel by a slower target model. By incorporating an inter-distribution transport map, the approach ensures unbiased acceleration while strictly preserving the target distribution across diverse systems and model pairings. Experimental results demonstrate speedups of 3–9×, offering both broad applicability and rigorous theoretical guarantees.

Extracting reaction mechanisms from trajectory data and efficiently sampling rare events remain challenging tasks. This work proposes a data-driven flow-matching framework that requires no prior knowledge of the system’s dynamics or stationary distribution. By minimizing a quadratic functional, the method jointly learns a vector flow field and a scalar potential to construct reactive pathways and reaction coordinates. Built upon a weighted Helmholtz–Hodge decomposition and reactive flow analysis, the approach remains well-defined even under non-Markovian collective variables and enables adaptive sampling. Numerical experiments demonstrate that the method generates accurate molecular flow trajectories and reliably computes reaction rate constants.

This study addresses the computational inefficiency bottleneck in long-timescale molecular dynamics simulations by proposing a machine learning force field framework based on Langevin flow mapping. The core innovation lies in incorporating a stochastic Langevin integrator into a machine learning model for the first time, fusing stochastic differential equations with deep learning techniques to enable direct learning of the stochastic integration process, thereby overcoming conventional small-timestep limitations. While faithfully preserving system dynamical properties and maintaining strong transferability, this approach achieves efficient large-timestep simulations, accelerating computation by an order of magnitude compared to existing methods.

This work addresses the challenge of reconstructing full spatiotemporal trajectories of gaseous reaction kinetics from sparse observational data by proposing a physics-guided diffusion prior sampling method. The approach embeds convection–reaction–diffusion partial differential equations as physical constraints within a diffusion model, enabling, for the first time, high-fidelity reconstruction of continuous and consistent spatiotemporal solutions. Under observation conditions closely mimicking real experimental settings—characterized by extreme data sparsity—the model not only accurately recovers the underlying spatiotemporal dynamics of the reaction process but also demonstrates strong generalization capabilities under unseen parameter regimes, thereby validating its effectiveness and robustness in extrapolating to new regions of the parameter space.

This work proposes the Coarse-Grained Boltzmann Generator (CG-BG) to address the challenge of efficient and unbiased sampling from the Boltzmann distribution in large molecular systems. By integrating flow-based generative models with potential of mean force (PMF) reweighting in a coarse-grained coordinate space, CG-BG uniquely unifies coarse-grained modeling with an exact importance-sampling-based reweighting scheme. The PMF is efficiently learned via force matching, enabling accurate representation of complex solvent-mediated interactions even under highly compressed representations. This approach preserves statistical unbiasedness while dramatically enhancing scalability, offering a novel and efficient pathway for sampling large-scale molecular systems.