arXiv subjects

Peter G. Bolhuis

Publications and source records attributed to Peter G. Bolhuis.

At least 19 recordsLinked to original sources

arXiv2026

QMaxCal: Path-Space Regularization for Open Quantum Control via Girsanov's Theorem

Reliable quantum control in the presence of decoherence requires policies that combat the effect of environmental noise on the controlled dynamics. Open quantum systems under continuous monitoring generate classical measurement records whose drift depends on the noise experienced by the system; the records of two evolutions sharing the same decoherence channels differ only in this drift, so Girsanov's theorem yields a closed-form, differentiable estimator of the KL divergence between their trajectory distributions. We instantiate this estimator with two physically motivated reference measures, yielding two regularizers that both drive the system toward states where the effects of decoherence are minimal: the Wiener KL (KL_W), which is empirically more effective under certain conditions on the noise model, and the drift-variance regularizer (R_DV), which works for all noise models. Both are qualitatively distinct from existing penalties on control fluence or smoothness: they penalize the observable consequences of control on the decoherence channels rather than the control amplitude itself. The regularizers outperform unregularized gradient-based and reinforcement-learning baselines across a range of open quantum systems -- including single- and multi-qubit benchmarks and a multi-qubit chain calibrated to a published snapshot of the IBM Kingston processor -- along several axes of evaluation: final-state fidelity, robustness to mismatch in the assumed noise model (gains grow from +17 pp at training noise to +27 pp under 2.5x noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50%, with ~16% gains on the calibrated IBM Kingston chain.

quant-ph↗

arXiv2026

Discovering Reaction Mechanisms with Transition Path Sampling-Based Active Learning of Machine-Learned Potentials

Machine-learned interatomic potentials (MLPs) provide near density functional theory (DFT) accuracy at reduced computational cost, but their reliability depends on representative training data and often deteriorates in transition-state regions governing rare events. We introduce an active-learning framework in which Transition Path Sampling (TPS) serves as a targeted data-generation engine for constructing MLPs accurate in barrier regions. TPS generates ensembles of unbiased reactive trajectories, and a committee-based uncertainty estimate identifies configurations for selective DFT labeling and retraining. Iterating this cycle systematically refines the potential energy surface in dynamically relevant regions, without the need of prior knowledge of the mechanism. Applied to electrochemical CO$_2$ reduction to CO on copper in explicit water, the approach removes nonphysical artifacts present in early models, achieves near-DFT energy and force accuracy, and enables stable long-time sampling of reactive pathways. Extended TPS simulations reveal multiple dynamically accessible protonation mechanisms. This work establishes TPS as an efficient and principled active-learning strategy for reactive molecular simulations at electrochemical interfaces.

physics.chem-ph↗

arXiv2026

General perturbative framework for kinetics of rare transitions in 1-dimensional active particle systems

We present a theoretical framework that enables investigating rare transitions in a general model of an active particle in an external potential, with the thermal Active Ornstein-Uhlenbeck Particle (AOUP) appearing as a special case. Using a projection-operator formalism, we compute transition rates perturbatively in two distinct asymptotic regimes. In the regime of small persistence times-where the activity evolves much faster than the particle's position-integrating out the activity reproduces the rates previously reported in the literature. In the opposite regime of large persistence times, we instead integrate out the position and obtain the corresponding rates analytically. Together, these asymptotic expansions uniquely specify a rational approximation that remains accurate across intermediate persistence times. As a result, we obtain an analytic expression for the rate valid across all persistence times and activity strengths in the rare-event limit, which are in excellent agreement with numerical simulations. The presented framework applies to rare transitions in a broad class of driven systems.

cond-mat.stat-mech↗

arXiv2026

An Always-Accepting Algorithm for Transition Path Sampling

We present a one-way shooting algorithm for transition path sampling that accepts every proposed trajectory, yet samples the correct transition path ensemble for systems with overdamped stochastic dynamics. The method is based on two key elements: a procedure to propose trajectories that are always reactive, and a reweighting scheme that corrects for the bias introduced by always accepting the proposed paths. This approach significantly improves the efficiency of transition path sampling by eliminating the cost associated with generating trajectories that are then rejected. We demonstrate the performances of the algorithm by investigating the formation of CO$_2$ clathrate hydrates along different reaction mechanisms, showing that the increased efficiency allows proper sampling of the formation of crystalline hydrates at temperatures and pressures that are difficult to access with conventional schemes.

physics.comp-ph↗

arXiv2026

Combining multiple interface set path ensembles with MBAR reweighting

We introduce a method to compute the reweighted path ensemble by combining transition interface sampling simulations conditioned on different collective variables. The approach is based on the Multistate Bennett Acceptance Ratio (MBAR) methodology applied to entire trajectories. Illustrating the technique with simple 2D potential models and a more complex host-guest system, we show that the statistics can significantly improve compared to a straightforward combination.

cond-mat.stat-mech↗

arXiv2025

Understanding Reaction Mechanisms from Start to Finish

Understanding mechanisms of rare but important events in complex molecular systems, such as protein folding or ligand (un)binding, requires accurately mapping transition paths from an initial to a final state. The committor is the ideal reaction coordinate for this purpose, but calculating it for high-dimensional, nonlinear systems has long been considered intractable. Here, we introduce an iterative path sampling strategy for computing the committor function for systems with high free energy barriers. We start with an initial guess to define isocommittor interfaces for transition interface sampling. The resulting path ensemble is then reweighted and used to train a neural network, yielding a more accurate committor model. This process is repeated until convergence, effectively solving the long-standing circular problem in enhanced sampling where a good reaction coordinate is needed to generate efficient sampling, and vice-versa. The final, converged committor model can be interrogated to extract mechanistic insights. We demonstrate the power of our method on a benchmark 2D potential and a more complex host-guest (un)binding process in explicit solvent.

physics.chem-ph↗

arXiv2025

Revisiting Shooting Point Monte Carlo Methods for Transition Path Sampling

Rare event sampling algorithms are essential for understanding processes that occur infrequently on the molecular scale, yet they are important for the long-time dynamics of complex molecular systems. One of these algorithms, transition path sampling (TPS), has become a standard technique to study such rare processes since no prior knowledge on the transition region is required. Most TPS methods generate new trajectories from old trajectories by selecting a point along the old trajectory, modifying its momentum in some way, and then ``shooting'' a new trajectory by integrating forward and backward in time. In some procedures, the shooting point is selected independently for each trial move, but in others, the shooting point evolves from one path to the next so that successive shooting points are related to each other. To account for this memory effect, we introduce a theoretical framework based on an extended ensemble that includes both paths and shooting indices. We derive appropriate acceptance rules for various path sampling algorithms in this extended formalism, ensuring the correct sampling of the transition path ensemble. Our framework reveals the need for amended acceptance criteria in the flexible-length aimless shooting and spring shooting methods.

physics.comp-ph↗

arXiv2025

Kinetic phase diagram for two-step nucleation in colloid-polymer mixtures

Two-step crystallization via a metastable intermediate phase is often regarded as a non-classical process that lies beyond the framework of classical nucleation theory (CNT). In this work, we investigate two-step crystallization in colloid-polymer mixtures via an intermediate liquid phase. Using CNT-based seeding simulations, we construct a kinetic phase diagram that identifies regions of phase space where the critical nucleus is either liquid or crystalline. These predictions are validated using transition path sampling simulations at nine different relevant state points. When the critical nucleus is liquid, crystallization occurs stochastically during the growth phase, whereas for a crystalline critical nucleus, the crystallization process happens pre-critically at a fixed nucleus size. We conclude that CNT-based kinetic phase diagrams are a powerful tool for understanding and predicting `non-classical' crystal nucleation mechanisms.

cond-mat.soft↗

arXiv2025

Optimal Rejection-Free Path Sampling

We propose an efficient novel path sampling-based framework designed to accelerate the investigation of rare events in complex molecular systems. A key innovation is the shift from sampling restricted path ensemble distributions, as in transition path sampling, to directly sampling the distribution of shooting points. This allows for a rejection-free algorithm that samples the entire path ensemble efficiently. Optimal sampling is achieved by applying a selection bias that is the inverse of the free energy along a reaction coordinate. The optimal reaction coordinate, the committor, is iteratively constructed as a neural network using AI for Molecular Mechanism Discovery (AIMMD), concurrently with the free energy profile, which is obtained through reweighting the sampled path ensembles. We showcase our algorithm on theoretical and molecular bechnmarks, and demonstrate how it provides at the same time molecular mechanism, free energy, and rates at a moderate computational cost.

physics.chem-ph↗

arXiv2024

Transition Path and Interface Sampling of Stochastic Schrödinger Dynamics

We study rare transitions in Markovian open quantum systems driven with Gaussian noise, applying transition path and interface sampling methods to trajectories generated by stochastic Schrödinger dynamics. Interface and path sampling offer insights into rare event transition mechanisms while simultaneously establishing a quantitative measure of the associated rate constant. Here, we extend their domain to systems described by stochastic Schrödinger equations. As a specific example, we explore a model of quantum Brownian motion in a quartic double well, consisting of a particle coupled to a Caldeira-Leggett oscillator bath, where we note significant departures from the Arrhenius law at low temperatures due to the presence of an anti-Zeno effect.

quant-ph↗

arXiv2023

Molecular free energies, rates, and mechanisms from data-efficient path sampling simulations

Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this limitation by collecting unbiased trajectories capturing the relevant events. Moreover, the integration of machine learning can boost the sampling while simultaneously learning a quantitative representation of the mechanism. Still, the resulting trajectories are by construction non-Boltzmann-distributed, preventing the calculation of free energies and rates. We developed an algorithm to approximate the equilibrium path ensemble from machine learning-guided path sampling data. At the same time, our algorithm provides efficient sampling, the mechanism, free energy, and rates of rare molecular events at a very moderate computational cost. We tested the method on the folding of the mini-protein chignolin. Our algorithm is straightforward and data-efficient, opening the door to applications on many challenging molecular systems.

physics.chem-ph↗

arXiv2023

Data-driven dynamical coarse-graining for condensed matter systems

Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in solution, where both the molecules(s) and the solvent dynamics needs to be integrated. This renders the simulations computationally costly and often unfeasible for physically or biologically relevant time scales. Standard coarse graining approaches are capable of reproducing equilibrium distributions and structural features but do not properly include the dynamics. In this work, we develop a stochastic data-driven coarse-graining method inspired by the Mori-Zwanzig formalism. This formalism shows that macroscopic systems with a large number of degrees of freedom can in principle be well described by a small number of relevant variables plus additional noise and memory terms. Our coarse-graining method consists of numerical integrators for the distinguished components of the system, where the noise and interaction terms with other system components are substituted by a random variable sampled from a data-driven model. Applying our methodology on three different systems -- a distinguished particle under a harmonic potential and under a bistable potential; and a dimer with two metastable configurations -- we show that the resulting coarse-grained models are not only capable of reproducing the correct equilibrium distributions but also the dynamic behavior due to temporal correlations and memory effects. Our coarse-graining method requires data from full-scale simulations to be parametrized, and can in principle be extended to different types of models beyond Langevin dynamics.

physics.comp-ph↗

arXiv2021

Autonomous artificial intelligence discovers mechanisms of molecular self-organization in virtual experiments

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Understanding the physical mechanisms that govern the formation of molecular complexes and crystals is key to controlling the assembly of nanomachines and new materials. We present an artificial intelligence (AI) agent that uses deep reinforcement learning and transition path theory to discover the mechanism of molecular self-organization phenomena from computer simulations. The agent adaptively learns how to sample complex molecular events and, on the fly, constructs quantitative mechanistic models. By using the mechanistic understanding for AI-driven sampling, the agent closes the learning cycle and overcomes time-scale gaps of many orders of magnitude. Symbolic regression condenses the mechanism into a human-interpretable form. Applied to ion association in solution, gas-hydrate crystal formation, and membrane-protein assembly, the AI agent identifies the many-body solvent motions governing the assembly process, discovers the variables of classical nucleation theory, and reveals competing assembly pathways. The mechanistic descriptions produced by the agent are predictive and transferable to close thermodynamic states and similar systems. Autonomous AI sampling has the power to discover assembly and reaction mechanisms from materials science to biology.

physics.chem-ph↗

arXiv2019

Approximating Free Energy and Committor Landscapes in Standard Transition Path Sampling using Virtual Interface Exchange

Transition path sampling (TPS) is a powerful technique for investigating rare transitions, especially when the mechanism is unknown and one does not have access to the reaction coordinate. Straightforward application of TPS does not directly provide the free energy landscape nor the kinetics, which motivated the development of path sampling extensions, such as transition interface sampling (TIS), and the reweighted paths ensemble (RPE), that are able to simultaneously access both kinetics and thermodynamics. However, performing TIS is more involved than TPS, and still requires (some) insight in the reaction to define interfaces. While packages that can efficiently compute path ensembles for TIS are now available, it would be useful to directly compute the free energy from a single TPS simulation. To achieve this, we developed an approximate method, denoted Virtual Interface Exchange, that makes use of the rejected pathways in a form of waste recycling. The method yields an approximate reweighted path ensemble that allows an immediate view of the free energy landscape from a single TPS, as well as enables a full committor analysis.

physics.chem-ph↗

arXiv2018

Ratchet-induced variations in bulk states of an active ideal gas

We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks, and thus exerts an influence of infinitely long range. As we show, crucial for having such a long-range influence is an external potential that is nonlinear. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameters in several limiting cases. While weakly active systems are often understood in terms of an effective temperature, we present an analytical solution that explicitly shows that this is not possible in the current setting. Instead, we rationalize our results by a simple transition state model, that presumes particles to cross the potential barrier by Arrhenius rates modified for activity. While this model does not quantitatively describe the difference in bulk densities for feasible parameter values, it does reproduce - in its regime of applicability - the complete power law behavior correctly.

cond-mat.soft↗

arXiv2018

Reaction rate theory for supramolecular kinetics: application to protein aggregation

Probing the reaction mechanisms of supramolecular processes in soft- and biological matter, such as protein aggregation, is inherently challenging. These processes emerge from the simultaneous action of multiple molecular mechanisms, each of which is associated with the rearrangement of a large number of weak bonds, resulting in a complex free energy landscape with many kinetic barriers. Reaction rate measurements of supramolecular processes at different temperatures can offer unprecedented insights into the underlying molecular mechanisms and their thermodynamic properties. However, to be able to interpret such measurements in terms of the underlying microscopic mechanisms, a key challenge is to establish which properties of the complex free energy landscapes are probed by the reaction rate. Here, we present a reaction rate theory for supramolecular kinetics based on Kramers rate theory for diffusive reactions over multiple kinetic barriers, and apply the results to protein aggregation. Using this framework and Monte Carlo simulations, we show that reaction rates for protein aggregation are of the Arrhenius-Eyring type and that the associated activation energies probe only one relevant barrier along the respective free energy landscapes. We apply this advancement to interpret, both in experiments and in coarse-grained computer simulations, reaction rate measurements of amyloid aggregation kinetics in terms of the underlying molecular mechanisms and associated thermodynamic signatures. Our results establish a general platform for probing the mechanisms and energetics of supramolecular phenomena in soft- and biological matter using the framework of chemical kinetics.

physics.bio-ph↗

arXiv2016

Multiscale simulations of anisotropic particles combining Brownian Dynamics and Green's Function Reaction Dynamics

The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic Molecular Dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P.G. Bolhuis and P.R. ten Wolde, J. Chem. Phys. {\bf 43}, 21: 214102 (2015)]. Here we extend this multiscale BD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm we discuss its performance. The rotational BD-GFRD multiscale method will open up the possibility for large scale simulations of e.g. protein signalling networks.

q-bio.MN↗

arXiv2016

Self-assembly of Microcapsules via Colloidal Bond Hybridization and Anisotropy

Particles with directional interactions are promising building blocks for new functional materials and may serve as models for biological structures. Mutually attractive nanoparticles that are deformable due to flexible surface groups, for example, may spontaneously order themselves into strings, sheets and large vesicles. Furthermore, anisotropic colloids with attractive patches can self-assemble into open lattices and colloidal equivalents of molecules and micelles. However, model systems that combine mutual attraction, anisotropy, and deformability have---to the best of our knowledge---not been realized. Here, we synthesize colloidal particles that combine these three characteristics and obtain self-assembled microcapsules. We propose that mutual attraction and deformability induce directional interactions via colloidal bond hybridization. Our particles contain both mutually attractive and repulsive surface groups that are flexible. Analogous to the simplest chemical bond, where two isotropic orbitals hybridize into the molecular orbital of H2, these flexible groups redistribute upon binding. Via colloidal bond hybridization, isotropic spheres self-assemble into planar monolayers, while anisotropic snowman-like particles self-assemble into hollow monolayer microcapsules. A modest change of the building blocks thus results in a significant leap in the complexity of the self-assembled structures. In other words, these relatively simple building blocks self-assemble into dramatically more complex structures than similar particles that are isotropic or non-deformable.

cond-mat.soft↗