arXiv subjects

Michele Invernizzi

Publications and source records attributed to Michele Invernizzi.

16 recordsLinked to original sources

arXiv2024

PLUMED Tutorials: a collaborative, community-driven learning ecosystem

In computational physics, chemistry, and biology, the implementation of new techniques in a shared and open source software lowers barriers to entry and promotes rapid scientific progress. However, effectively training new software users presents several challenges. Common methods like direct knowledge transfer and in-person workshops are limited in reach and comprehensiveness. Furthermore, while the COVID-19 pandemic highlighted the benefits of online training, traditional online tutorials can quickly become outdated and may not cover all the software's functionalities. To address these issues, here we introduce ``PLUMED Tutorials'', a collaborative model for developing, sharing, and updating online tutorials. This initiative utilizes repository management and continuous integration to ensure compatibility with software updates. Moreover, the tutorials are interconnected to form a structured learning path and are enriched with automatic annotations to provide broader context. This paper illustrates the development, features, and advantages of PLUMED Tutorials, aiming to foster an open community for creating and sharing educational resources.

physics.ed-ph↗

arXiv2024

Advanced simulations with PLUMED: OPES and Machine Learning Collective Variables

Many biological processes occur on time scales longer than those accessible to molecular dynamics simulations. Identifying collective variables (CVs) and introducing an external potential to accelerate them is a popular approach to address this problem. In particular, $\texttt{PLUMED}$ is a community-developed library that implements several methods for CV-based enhanced sampling. This chapter discusses two recent developments that have gained popularity in recent years. The first is the On-the-fly Probability Enhanced Sampling (OPES) method as a biasing scheme. This provides a unified approach to enhanced sampling able to cover many different scenarios: from free energy convergence to the discovery of metastable states, from rate calculation to generalized ensemble simulation. The second development concerns the use of machine learning (ML) approaches to determine CVs by learning the relevant variables directly from simulation data. The construction of these variables is facilitated by the $\texttt{mlcolvar}$ library, which allows them to be optimized in Python and then used to enhance sampling thanks to a native interface inside $\texttt{PLUMED}$. For each of these methods, in addition to a brief introduction, we provide guidelines, practical suggestions and point to examples from the literature to facilitate their use in the study of the process of interest.

physics.comp-ph↗

arXiv2024

Efficient mapping of phase diagrams with conditional Boltzmann Generators

The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative stability between phases based on their free energy is a daunting task, as traditional free energy estimators require a large amount of simulation data to obtain uncorrelated equilibrium samples over a grid of thermodynamic states. In this work, we develop deep generative machine learning models based on the Boltzmann Generator approach for entire phase diagrams, employing normalizing flows conditioned on the thermodynamic states, e.g., temperature and pressure, that they map to. By training a single normalizing flow to transform the equilibrium distribution sampled at only one reference thermodynamic state to a wide range of target temperatures and pressures, we can efficiently generate equilibrium samples across the entire phase diagram. Using a permutation-equivariant architecture allows us, thereby, to treat solid and liquid phases on the same footing. We demonstrate our approach by predicting the solid-liquid coexistence line for a Lennard-Jones system in excellent agreement with state-of-the-art free energy methods while significantly reducing the number of energy evaluations needed.

cond-mat.stat-mech↗

arXiv2023

Rigid Body Flows for Sampling Molecular Crystal Structures

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

cs.LG↗

arXiv2022

Skipping the Replica Exchange Ladder with Normalizing Flows

We combine replica exchange (parallel tempering) with normalizing flows, a class of deep generative models. These two sampling strategies complement each other, resulting in an efficient strategy for sampling molecular systems characterized by rare events, which we call learned replica exchange (LREX). In LREX, a normalizing flow is trained to map the configurations of the fastest-mixing replica into configurations belonging to the target distribution, allowing direct exchanges between the two without the need to simulate intermediate replicas. This can significantly reduce the computational cost compared to standard replica exchange. The proposed method also offers several advantages with respect to Boltzmann generators that directly use normalizing flows to sample the target distribution. We apply LREX to some prototypical molecular dynamics systems, highlighting the improvements over previous methods.

physics.comp-ph↗

arXiv2022

Rare Event Kinetics from Adaptive Bias Enhanced Sampling

We introduce a novel enhanced sampling approach named OPES flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the On-the-fly-Probability-Enhanced-Sampling (OPES) approach [Invernizzi and Parrinello, JPC Lett. 2020], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double well potential, conformational transition in the alanine dipeptide in gas phase, and the folding and unfolding of the chignolin polypeptide in aqueous environment. From extensive tests, we show that the calculation of accurate kinetics not only requires the transition state to be bias-free, but the amount of bias deposited should also not exceed the effective barrier height measured along the chosen collective variables. In this vein, the possibility of computing rates from biasing suboptimal order parameters has also been explored. Furthermore, we describe the choice of optimum parameter combinations for obtaining accurate results from limited computational effort.

physics.chem-ph↗

arXiv2022

Exploration vs Convergence Speed in Adaptive-bias Enhanced Sampling

In adaptive-bias enhanced sampling methods, a bias potential is added to the system to drive transitions between metastable states. The bias potential is a function of a few collective variables and is gradually modified according to the underlying free energy surface. We show that when the collective variables are suboptimal, there is an exploration-convergence tradeoff, and one must choose between a quickly converging bias that will lead to fewer transitions, or a slower to converge bias that can explore the phase space more efficiently but might require a much longer time to produce an accurate free energy estimate. The recently proposed On-the-fly Probability Enhanced Sampling (OPES) method focuses on fast convergence, but there are cases where fast exploration is preferred instead. For this reason, we introduce a new variant of the OPES method that focuses on quickly escaping metastable states, at the expense of convergence speed. We illustrate the benefits of this approach on prototypical systems and show that it outperforms the popular metadynamics method.

physics.comp-ph↗

arXiv2021

OPES: On-the-fly Probability Enhanced Sampling Method

Molecular simulations are playing an ever increasing role, finding applications in fields as varied as physics, chemistry, biology and material science. However, many phenomena of interest take place on time scales that are out of reach of standard molecular simulations. This is known as the sampling problem and over the years several enhanced sampling methods have been developed to mitigate this issue. We propose a unified approach that puts on the same footing the two most popular families of enhanced sampling methods, and paves the way for novel combined approaches. The on-the-fly probability enhanced sampling method provides an efficient implementation of such generalized approach, while also focusing on simplicity and robustness.

physics.comp-ph↗

arXiv2021

Collective Variables for the Study of Crystallization

The phenomenon of solidification of a substance from its liquid phase is of the greatest practical and theoretical importance, and atomistic simulations can provide precious information towards its understanding and control. Unfortunately, the time scale for crystallization is much larger than what can be explored in standard simulations. Enhanced sampling methods can overcome this time scale hurdle. Here we employ the on-the-fly probability enhanced sampling method that is a recent evolution of metadynamics. This method, like many others, relies on the definition of appropriate collective variables able to capture the slow degrees of freedom. To this effect we introduce collective coordinates of general applicability to crystallization simulations. They are based on the peaks of the three-dimensional structure factor that are combined non-linearly via the Deep Linear Discriminant Analysis machine learning method. We apply the method to the study of crystallization of a multicomponent system, Sodium Chloride and a molecular system, Carbon Dioxide.

cond-mat.soft↗

arXiv2020

Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration

Accurate thermodynamic simulations of correlated fermions using path integral Monte Carlo (PIMC) methods are of paramount importance for many applications such as the description of ultracold atoms, electrons in quantum dots, and warm-dense matter. The main obstacle is the fermion sign problem (FSP), which leads to an exponential increase in computation time both with increasing the system-size and with decreasing temperature. Very recently, Hirshberg et al. [J. Chem. Phys. 152, 171102 (2020)] have proposed to alleviate the FSP based on the Bogoliubov inequality. In the present work, we extend this approach by adding a parameter that controls the perturbation, allowing for an extrapolation to the exact result. In this way, we can also use thermodynamic integration to obtain an improved estimate of the fermionic energy. As a test system, we choose electrons in 2D and 3D quantum dots and find in some cases a speed-up exceeding 10^6 , as compared to standard PIMC, while retaining a relative accuracy of $\sim0.1\%$. Our approach is quite general and can readily be adapted to other simulation methods.

physics.comp-ph↗

arXiv2020

A Unified Approach to Enhanced Sampling

The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand methods such as umbrella sampling and metadynamics that build a bias potential based on few order parameters or collective variables. On the other hand, tempering methods such as replica exchange that combine different thermodynamic ensembles in one single expanded ensemble. We instead adopt a unifying perspective, focusing on the target probability distribution sampled by the different methods. This allows us to introduce a new class of collective-variables-based bias potentials that can be used to sample any of the expanded ensembles normally sampled via replica exchange. We also provide a practical implementation, by properly adapting the iterative scheme of the recently developed on-the-fly probability enhanced sampling method [Invernizzi and Parrinello, J. Phys. Chem. Lett. 11.7 (2020)], which was originally introduced for metadynamics-like sampling. The resulting method is very general and can be used to achieve different types of enhanced sampling. It is also reliable and simple to use, since it presents only few and robust external parameters and has a straightforward reweighting scheme. Furthermore, it can be used with any number of parallel replicas. We show the versatility of our approach with applications to multicanonical and multithermal-multibaric simulations, thermodynamic integration, umbrella sampling, and combinations thereof.

physics.comp-ph↗

arXiv2020

Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality

We present a method for performing path integral molecular dynamics (PIMD) simulations for fermions and address its sign problem. PIMD simulations are widely used for studying many-body quantum systems at thermal equilibrium. However, they assume that the particles are distinguishable and neglect bosonic and fermionic exchange effects. Interacting fermions play a key role in many chemical and physical systems, such as electrons in quantum dots and ultracold trapped atoms. A direct sampling of the fermionic partition function is impossible using PIMD since its integrand is not positive definite. We show that PIMD simulations for fermions are feasible by employing our recently developed method for bosonic PIMD and reweighting the results to obtain fermionic expectation values. The approach is tested against path integral Monte Carlo (PIMC) simulations for up to 7 electrons in a two-dimensional quantum dot for a range of interaction strengths. However, like PIMC, the method suffers from the sign problem at low temperatures. We propose a simple approach for alleviating it by simulating an auxiliary system with a larger average sign and obtaining an upper bound to the energy of the original system using the Bogoliubov inequality. This allows fermions to be studied at temperatures lower than would otherwise have been feasible using PIMD, as demonstrated in the case of a three-electron quantum dot. Our results extend the boundaries of PIMD simulations of fermions and will hopefully stimulate the development of new approaches for tackling the sign problem.

physics.chem-ph↗

arXiv2020

Rethinking Metadynamics: from bias potentials to probability distributions

Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is function of a selected number of collective variables. We propose here a change in perspective that shifts the focus from the bias to the probability distribution reconstruction, while keeping some of the key characteristics of metadynamics, such as the flexible on-the-fly adjustments to the free energy estimate. The result is an enhanced sampling method that presents a drastic improvement in convergence speed, especially when dealing with suboptimal and/or multidimensional sets of collective variables. The method is especially robust and easy to use, in fact it requires only few simple parameters to be set, and it has a straightforward reweighting scheme to recover the statistics of the unbiased ensemble. Furthermore it gives more control on the desired exploration of the phase space, since the deposited bias is not allowed to grow indefinitely and it does not push the simulation to uninteresting high free energy regions. We demonstrate the performance of the method in a number of representative examples.

physics.comp-ph↗

arXiv2019

Making the best of a bad situation: a multiscale approach to free energy calculation

Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently and reconstruct the free energy landscape. In methods like metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal with the non-ideal situation of a system in which some slow modes are not accelerated. We propose a two-step approach in which, by taking into account the residual multiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free energy difference between metastable states, based on the recently proposed variationally enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture.

physics.comp-ph↗

arXiv2018

Enhanced sampling of transition states

The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes enhanced sampling methods are used. While many such methods are able to obtain sufficient sampling in order to draw the free energy, the transition states are often sparsely sampled. We propose an approach based on the Variationally Enhanced Sampling Method to enhance sampling in the transition region. To this effect, we introduce a dynamic target distribution which uses the derivative of the instantaneous free energy surface to locate the transition regions on the fly and modulate the probability of sampling different regions. Finally, we exemplify the effectiveness of this approach in enriching the number of configurations in the transition state region in the cases of a chemical reaction and of a nucleation process.

physics.chem-ph↗

arXiv2015

Superlubric-Pinned Transition in Sliding Incommensurate Colloidal Monolayers

Two-dimensional (2D) crystalline colloidal monolayers sliding over a laser-induced optical lattice recently emerged as a new tool for the study of friction between ideal crystal surfaces. Here we focus in particular on static friction, the minimal sliding force necessary to depin one lattice from the other. If the colloid and the optical lattices are mutually commensurate, the colloid sliding is always pinned by static friction; but when they are incommensurate the presence or absence of pinning can be expected to depend upon the system parameters. If a 2D analogy to the mathematically established Aubry transition of one-dimensional systems were to hold, an increasing periodic corrugation strength $U_0$ should turn an initially free-sliding monolayer into a pinned state through a well-defined dynamical phase transition. We address this problem by the simulated sliding of a realistic model 2D colloidal lattice, confirming the existence of a clear and sharp superlubric-pinned transition for increasing corrugation strength. Unlike the 1D Aubry transition which is continuous, the 2D transition exhibits a definite first-order character. With no change of symmetry, the transition entails a structural character, with a sudden increase of the colloid-colloid interaction energy, accompanied by a compensating downward jump of the colloid-corrugation energy. The transition value for the corrugation amplitude $U_0$ depends upon the misalignment angle $θ$ between the optical and the colloidal lattices, superlubricity surviving until larger corrugations for angles away from the energetically favored orientation, which is itself generally slightly misaligned, as shown in recent work. The observability of the superlubric-pinned colloid transition is proposed and discussed.

cond-mat.mes-hall↗