On-the-fly N${^2}$AMD (Neural network NAMD), a machine learning framework that makes on-the-fly NAMD in solids a reality, by employing an equivariant neural network to predict the system Hamiltonian, delivers excited-state energies, forces, and non-adiabatic coupling vectors at a fraction of the cost of ab initio calculations.
Abstract
Simulating the coupled, nonequilibrium dynamics of electrons and nuclei is a central challenge in chemistry, physics, and materials science, governing phenomena from photocatalysis to quantum information. The primary bottleneck has been the lack of a general, accurate, and efficient method for modeling the complete excited-state landscape: the potential energy surfaces, forces, and non-adiabatic couplings for multiple electronic states. While machine learning has revolutionized ground-state simulations and shown promise for excited states in molecules, a unified framework that solves the complete multi-state problem for general condensed matter systems has remained elusive. Here we introduce on-the-fly N${^2}$AMD (Neural network NAMD), a machine learning framework that makes on-the-fly NAMD in solids a reality. By employing an equivariant neural network to predict the system Hamiltonian, the framework delivers excited-state energies, forces, and non-adiabatic coupling vectors at a fraction of the cost of ab initio calculations. Crucially, it allows simulations with hybrid functional accuracy, a level of approach previously inaccessible for NAMD. We showcase its capabilities with three topical examples: correcting order-of-magnitude errors in carrier dynamics predicted by conventional procedure in a MoS$_2$/WS$_2$ heterostructure, simulating previously inaccessible photoinduced ferroelectric switching, and capturing real-time polaron formation in TiO$_2$ at the hybrid-functional level. On-the-fly N${^2}$AMD moves beyond the limitations of equilibrium theory, establishing a new paradigm for the predictive, first-principles design of materials operating far from equilibrium.
We introduce quantum Monte Carlo (QMC)-trained multi-state machine-learned (ML) force fields for nonadiabatic excited-state dynamics, targeting photochemical processes in which the electronic character changes along the reaction path and a consistent correlated description is required. In this framework, variational Monte Carlo wave functions combine compact selected configuration-interaction expansions with a Jastrow factor that explicitly accounts for dynamical correlation, while neural networks convert the stochastic QMC data into smooth potential energy surfaces for large surface-hopping ensembles. We apply this approach to azomethane, a demanding test case involving torsional relaxation through conical-intersection regions and C--N bond dissociation on the hot ground state. Benchmark calculations support the accuracy of the QMC reference data and show robust force convergence across isomerization and dissociation geometries. The QMC-trained dynamics preserves the expected photoisomerization mechanism, strongly reduces the excessive C--N breaking obtained with complete active space self-consistent field, and predicts a small but non-negligible prompt dissociation component after internal conversion, with a timescale consistent with femtosecond-resolved mass-spectrometry experiments. These results establish QMC-ML as a practical route to nonadiabatic photochemical dynamics with accurate wave-function reference data.
Alfonso Annarelli, Emiel Slootman, C. Filippi· 0 citations
We propose a physics-informed neural network (PINN) scheme for designing shortcuts to adiabaticity in a three-level non-Hermitian quantum system. The PINN is used to solve an inverse control problem in which the state amplitudes and the auxiliary driving field are learned simultaneously from the Schrödinger residual, the initial and target population constraints and a probability conservation constraint on the control pulse. The learned compensation field counteracts the loss of the intermediate state and enables high-fidelity population inversion in an open-system setting. Importantly, the imposed probability conservation is treated as an auxiliary constraint along the learned trajectory rather than as an intrinsic property of the non-Hermitian Hamiltonian. Under this constrained evolution, the Hamiltonian expectation value evaluated on the obtained state remains real within numerical accuracy. Numerical simulations and independent propagation with the fitted control field verify the population inversion and exhibit strong generalization capability over a range of coupling strengths and dissipation rates, as verified by retraining the network independently for each parameter set. The results demonstrate that PINNs provide a flexible inverse design tool for non-Hermitian shortcut to adiabaticity protocols when the governing dynamics and physical constraints are explicitly incorporated into the loss function.
Ming Liu, Feng Huang, Siqi Zhang et al.· Entropy· 0 citations
Investigating ultrafast electron–nuclear dynamics in molecules requires robust theoretical methods that offer predictive capabilities beyond interpretation purposes. However, the vast number of electronic and nuclear degrees of freedom often prevents an accurate description of chemical systems on classical computers. To address these challenges, hybrid approaches combining quantum and classical computing can leverage the strengths of both to enhance the computational efficiency and fully exploit hardware capabilities. In this work, we perform excited-state molecular dynamics simulations of the formaldimine molecule by combining the surface hopping nonadiabatic molecular dynamics technique with quantum algorithms. We replace conventional electronic energy and overlap calculations with the variational quantum deflation (VQD) algorithm and the Hadamard test, respectively, employing a configuration state function (CSF) spin-restricted ansatz. Finally, we evaluate the accuracy and feasibility of three different gradient calculation approaches integrated with the quantum computing components, demonstrating the advantages of an analytical gradient method over finite difference approaches for hybrid quantum–classical integration.
Silvia Riera-Villapún, Jaime Scharfhausen-Curiel, Juan Luis Sánchez Toural et al.· Journal of Physical Chemistr...· 0 citations
One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. K\"uhne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.
Jan Wilhelm, Anna-Sophia Hehn, Hossam Elgabarty et al.· 1 citation· ⚡1
Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.
J. Rigo, B. J. Wurst, R. Nutakki et al.· 0 citations
Ultrafast photoexcitation offers a controllable route to steer structural dynamics in solids, yet predicting how nonequilibrium electronic excitation drives lattice motion across extended spatial and temporal scales remains a major computational challenge. Here we introduce time-dependent ab-initio propagation with electronic machine learning (TDAP-eML), a framework that explicitly incorporates electronic evolution into scalable simulations of photoexcitation-induced lattice dynamics. By integrating machine-learned electronic structure with atomistic propagation, TDAP-eML describes how photoexcitation reshapes the evolving energy landscapes and forces governing structural motion. Across representative examples including silicon and FeSe, the framework reproduces key photoexcited lattice responses obtained from first-principles time-dependent density functional theory calculations and captures coherent phonon dynamics together with their dependence on excitation conditions. Its computational advantage increases with system size, reaching nearly three orders of magnitude reduction in computational cost for the large systems examined. TDAP-eML thus establishes a scalable framework for coupled electronic and lattice evolution, linking nonequilibrium excitation to photoinduced forces, predictive structural dynamics, and experimentally accessible observables.
Leyu Cai, Yunzhe Jia, Daqiang Chen et al.· 0 citations