Research Outcomes

A variety of enhanced sampling methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets -- ideally incorporating information about physical pathways and transition states -- which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of enhanced sampling simulations in trajectory space via the metadynamics of paths algorithm. The approach is expected to provide a general and efficient way to generate efficient high quality d CVs for the fast prediction of free energy landscapes. We demonstrate our approach on two numerical examples, a two-dimensional model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice. Link to the paper: https://academic.oup.com/pnasnexus/article/3/4/pgae159/7644514#447699016 Pre-print: https://arxiv.org/abs/2311.05571

The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise—one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. The adaptive cost control is performed by first setting the required accuracy according to the progress of the optimization, and then choosing the minimum number of measurement shots and their distribution such that the required accuracy is satisfied. We demonstrate that SubsCoRe significantly improves the efficiency of SMO, and outperforms the state-of-the-art methods. Link to the paper: https://openreview.net/pdf?id=dSrdnhLS2h

A significant aspect of the economic performance and safety of a nuclear reactor involves maintaining the integrity of the fuel rods, which are susceptible to Turbulence-Induced Vibrations (TIV) resulting from the axial flow of the coolant. TIV can instigate severe repercussions, including structural damage such as fatigue and wear. TIV can be studied numerically, using Fluid–Structure Interaction( FSI) simulations. However, high-resolution approaches are computationally too expensive to use for complex FSI simulations, while Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations severely underpredict the displacement amplitudes of the vibrations as they only resolve the mean flow. Evolving from this shortfall, this paper focuses on a recently developed Anisotropic Pressure Fluctuation Model (AniPFM). This model generates a synthetic velocity fluctuations field, which is used to solve for the pressure fluctuations. Using this model, together with URANS, is a possible way to simulate the excitation mechanisms of TIV of fuel rods in a computationally cheaper way. While previous research has highlighted the potential of this model, there are parameters, definitions, and constants whose impacts on the model are not yet fully understood. Therefore, a comprehensive effort is undertaken to fine-tune the model, optimize its performance, improve understanding of it and further validate it. This is done by applying AniPFM to both pure flow and FSI cases, using high-resolution numerical and experimental data as reference and for comparison. With the optimized model, a substantial decrease in average difference from the experimental data is found for the FSI case under consideration, when compared with the unoptimized version of AniPFM. Link to the paper: https://doi.org/10.1063/5.0235792

We present a novel methodology for modeling the influence of the unresolved scales of turbulence for sub-grid modeling. Our approach employs the differentiable physics paradigm in deep learning, allowing a neural network to interact with the differential equation evolution and performing an a posteriori optimization by incorporating the solver into the training iteration (an approach known as solver-in-the-loop), thus departing from the conventional a priori instantaneous training approach. Our method ensures that the model is exposed to equations-informed input distributions, accounting for prior corrections and often leading to more accurate and stable time evolution. We present results of our methodology applied to a shell model of turbulence, and we discuss further potential applications to Navier-Stokes equations. Pre-print: https://arxiv.org/abs/2411.13194

Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose its Bayesian variant, where Gaussian processes with appropriate kernels are used to estimate the gradient of the VQE objective. Our Bayesian PSR offers flexible gradient estimation from observations at arbitrary locations with uncertainty information and reduces to the generalized PSR in special cases. In stochastic gradient descent (SGD), the flexibility of Bayesian PSR allows the reuse of observations in previous steps, which accelerates the optimization process. Furthermore, the accessibility to the posterior uncertainty, along with our proposed notion of gradient confident region (GradCoRe), enables us to minimize the observation costs in each SGD step. Our numerical experiments show that the VQE optimization with Bayesian PSR and GradCoRe significantly accelerates SGD and outperforms the state-of-the-art methods, including sequential minimal optimization. Pre-print: https://arxiv.org/abs/2502.02625

Molecular dynamics (MD)-based path sampling algorithms are a very important class of methods used to study the energetics and kinetics of rare (bio)molecular events. They sample the highly informative but highly unlikely reactive trajectories connecting different metastable states of complex (bio)molecular systems. The metadynamics of paths (MoP) method proposed by Mandelli, Hirshberg, and Parrinello [Pys. Rev. Lett. 125 2, 026001 (2020)] is based on the Onsager-Machlup path integral formalism. This provides an analytical expression for the probability of sampling stochastic trajectories of given duration. In practice, the method samples reactive paths via metadynamics simulations performed directly in the phase space of all possible trajectories. Its parallel implementation is in principle infinitely scalable, allowing arbitrarily long trajectories to be simulated. Paving the way for future applications to study the thermodynamics and kinetics of protein-ligand (un)binding, a problem of great pharmaceutical interest, we present here the efficient implementation of MoP in the HPC-oriented biomolecular simulation software GROMACS. Our benchmarks on a membrane protein (150,000 atoms) show an unprecedented weak scaling parallel efficiency of over 70% up to 3200 GPUs on the pre-exascale JUWELS Booster machine at the Jülich Supercomputing Center. pre-print: https://arxiv.org/abs/2501.11962

We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to model the non-ideal sharp interface of the droplet coupled with the inner and outer fluids, simulated with the lattice Boltzmann scheme. We further introduce an interaction force to model the wetting interactions of the droplet with the solid: this interaction force is designed with the key computational advantage of providing a regularization of the interface profile close to the contact line, avoiding abrupt curvature changes that could otherwise cause numerical instabilities. The proposed model substantially improves earlier immersed boundary - lattice Boltzmann models for wetting in that it allows a description of an ample variety of wetting interactions, ranging from hydrophobic to hydrophilic cases, without the need for any pre-calibration study on model parameters to be used. Model validations against theoretical results for droplet shape at equilibrium and scaling laws for droplet spreading dynamics are addressed. Link to the paper: https://arxiv.org/abs/2503.20605

Investigating critical phenomena or phase transitions is of high interest in physics and chemistry, for which Monte Carlo (MC) simulations, a crucial tool for numerically analyzing macroscopic properties of given systems, are often hindered by an emerging divergence of correlation length -- known as scale invariance at criticality (SIC) in the renormalization group theory. SIC causes the system to behave the same at any length scale, from which many existing sampling methods suffer: long-range correlations cause critical slowing down in Markov chain Monte Carlo (MCMC), and require intractably large receptive fields for generative samplers. In this paper, we propose a Renormalization-informed Generative Critical Sampler (RiGCS) -- a novel sampler specialized for near-critical systems, where SIC is leveraged as an advantage rather than a nuisance. Specifically, RiGCS builds on MultiLevel Monte Carlo (MLMC) with Heat Bath (HB) algorithms, which perform ancestral sampling from low-resolution to high-resolution lattice configurations with site-wise-independent conditional HB sampling. Although MLMC-HB is highly efficient under exact SIC, it suffers from a low acceptance rate under slight SIC violation. Notably, SIC violation always occurs in finite-size systems, and may induce long-range and higher-order interactions in the renormalized distributions, which are not considered by independent HB samplers. RiGCS enhances MLMC-HB by replacing a part of the conditional HB sampler with generative models that capture those residual interactions and improve the sampling efficiency. Our experiments show that the effective sample size of RiGCS is a few orders of magnitude higher than state-of-the-art generative model baselines in sampling configurations for 128x128 two-dimensional Ising systems. Link to the paper: https://arxiv.org/abs/2503.08918

In this paper, we develop a lattice Boltzmann scheme based on the Vielbein formalism for the study of fluid flows on spherical surfaces. The Vielbein vector field encodes all details related to the geometry of the underlying spherical surface, allowing the velocity space to be treated as on the Cartesian space. The resulting Boltzmann equation exhibits inertial (geometric) forces that ensure that fluid particles follow paths that remain on the spherical manifold, which we compute by projection onto the space of Hermite polynomials. Due to the point-dependent nature of the advection velocity in the polar coordinate θ, exact streaming is not feasible, and we instead employ finite-difference schemes. We provide a detailed formulation of the lattice Boltzmann algorithm, with particular attention to boundary conditions at the north and south poles. We validate our numerical implementation against two analytical solutions of the Navier-Stokes equations derived in this work: the propagation of sound and shear waves. Additionally, we assess the robustness of the scheme by simulating the compressible flow of an axisymmetric shock wave and analyzing vortex dynamics on the spherical surface. https://journals.aps.org/prfluids/pdf/10.1103/k6z2-rqdw

We investigate static and dynamical aspects of string breaking in a Z2 lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using tensor network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both tensor networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute toward the static charges and screen them, which leads to the breaking of the flux tube. https://journals.aps.org/prd/pdf/10.1103/r6sr-dv13

Turbulent flows laden with small bubbles are ubiquitous in many natural and industrial environments. From the point of view of numerical modeling, to be able to handle a very large number of small bubbles in direct numerical simulations, one traditionally relies on the one-way coupling paradigm. There, bubbles are passively advected and are non-interacting, implicitly assuming dilute conditions. Here, we study bubbles that are four-way coupled, where both the feedback on the fluid and excluded-volume interactions between bubbles are taken into account. We find that, while the back-reaction from the bubble phase onto the fluid phase remains energetically small under most circumstances, the excluded-volume interactions between bubbles can have a significant influence on the Lagrangian statistics of the bubble dynamics. We show that as the volume fraction of bubbles increases, the preferential concentration of bubbles in filamentary high-vorticity regions decreases as these strong vortical structures get filled up; this happens at a volume fraction of around one percent for Reλ=O(102) . We furthermore study the influence on the Lagrangian velocity structure function as well as pair dispersion, and find that, while the mean dispersive behavior remains close to that obtained from one-way coupling simulations, some evident signatures of bubble collisions can be retrieved from the structure functions and the distribution of the dispersion, even at very small volume fractions. This work not only teaches us about the circumstances under which four-way coupling becomes important, but also opens up new directions towards probing and ultimately manipulating coherent vortical structures in small-scale turbulence using bubbles. https://arxiv.org/pdf/2510.03968

We investigate how turbulence is reshaped by the presence of externally forced light particles, using high-resolution direct numerical simulations with four-way coupling. The particles are subject to an oscillatory force that in turn locally affects the fluid flow through momentum exchange at the position of the particles. Since the light particles preferentially concentrate in high vorticity regions, this leads to an intricate preferential turbulence modulation. We show that through this modulation, the forced light particles strongly reduce the intermittency of the flow, shedding new light on the delicate relationship between vortex filaments and turbulence intermittency. https://arxiv.org/pdf/2508.06660

We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to model the nonideal sharp interface of the droplet coupled with the inner and outer fluids, simulated with the lattice Boltzmann scheme. We further introduce an interaction force to model the wetting interactions of the droplet with the solid at mesoscale: this interaction force is designed with the key computational advantage of providing a regularization of the interface profile close to the contact line, avoiding abrupt curvature changes that could otherwise cause numerical instabilities. The proposed model substantially improves earlier immersed boundary–lattice Boltzmann models for wetting in that it allows a description of an ample variety of wetting interactions, ranging from hydrophobic to hydrophilic cases, without the need for any precalibration study on model parameters to be used. Model validations against analytical results for droplet shape at equilibrium and scaling laws for droplet spreading dynamics are addressed. DOI: 10.1103/mp3p-8j22

We explore the potential of Data-Assimilation (DA) within the multi-scale framework of a shell model of turbulence, with a focus on the Ensemble Kalman Filter (EnKF). The central objective is to understand how measuring mesoscales (i.e., inertial-range scales) enhances the prediction of both large-scale and small-scale intermittent variables, by systematically varying observation frequency and the set of measured scales. We demonstrate that measurements conducted at frequencies that exceed those of the observed scales enable full synchronization of larger scales, provided that at least two adjacent mesoscale are measured. In addition, we benchmark the EnKF against two other DA methods, namely Nudging and Ensemble 4D-Var. EnKF is clearly superior to the former, and comparable with the latter but achieving the result with a lower computational complexity. Moreover, our results underscore the need for a tailored, scale-aware inflation technique to stabilize the assimilation process, preventing filter divergence and ensuring robust convergence. https://arxiv.org/pdf/2507.15626

We introduce a novel technique to numerically calculate Rényi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the ϕ4 scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size. DOI: 10.1103/PhysRevLett.134.151601