Research Outcomes

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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