Four-Dimensional-Spacetime Atomistic Artificial Intelligence Models

Abstract

We demonstrate that AI can learn atomistic systems in the four-dimensional (4D) spacetime. For this, we introduce the 4D-spacetime GICnet model, which for the given initial conditions (nuclear positions and velocities at time zero) can predict nuclear positions and velocities as a continuous function of time up to the distant future. Such models of molecules can be unrolled in the time dimension to yield long-time high-resolution molecular dynamics trajectories with high efficiency and accuracy. 4D-spacetime models can make predictions for different times in any order and do not need a stepwise evaluation of forces and integration of the equations of motions at discretized time steps, which is a major advance over traditional, cost-inefficient molecular dynamics. These models can be used to speed up dynamics, simulate vibrational spectra, and obtain deeper insight into nuclear motions, as we demonstrate for a series of organic molecules.

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

“…MLatom also provides the flexibility of training custom models based on kernel ridge regression (KRR) for a given set of input vectors x or XYZ coordinates and any labels y . , If XYZ coordinates are provided, they can be transformed in one of the several supported descriptors (e.g., inverse internuclear distances and their version normalized relative to the equilibrium structure (RE) and the Coulomb matrix). The user can choose from one of the implemented kernel functions, including the linear, ,, Gaussian, ,, exponential, ,, Laplacian, ,, and Matérn ,− as well as periodic ,, and decaying periodic ,, functions, which are summarized in Table . These kernel functions k ( x , x j ; h ) are key components required to solve the KRR problem of finding the regression coefficients α of the approximating function f̂ ( x ; h ) of the input vector x : , f̂ ( x ; h ) = ∑ j = 1 N tr α j k ( x , boldx j ; h ) …”

“…The IR spectra are obtained via the fast Fourier transform using the autocorrelation function of dipole moment , with our own implementation . The power spectra only need the fast Fourier transform, which is also implemented in MLatom.…”

Energy-conserving molecular dynamics is not energy conserving

“…30,31 Analysis of the TBE total energies may be thus used as an alternative measure of the accuracy of the used potential, e.g., when MD is propagated with forces evaluated as negative derivatives of ML potential (simulation-energy-conserving MD). 30,31 Moreover, the TBE analysis can be conveniently used as a standard universal way to evaluate MD trajectories also in cases when the MD trajectories were generated without using a potential but, e.g., when the nuclear coordinates are predicted directly by ML as a function of time 11,32,33 or when MD is propagated with force components predicted separately by ML (simulation-energy non-conserving MD). 10 Such evaluations can be helpful in choosing an appropriate affordable model and simulation strategy (Fig.…”

“…In context of ML potentials, it may be convenient to choose the reference potential used to generate the training data for ML as TBE; this allows to gauge the quality of ML potential in performing real MD simulations rather than by simply benchmarking their accuracy in potential energies and forces as is commonly done 30,31 . Analysis of the TBE total energies may be used as a standard universal way to evaluate MD trajectories regardless how they were obtained, e.g., directly predicted by ML 11,32,33 or by propagating MD with forces evaluated as negative derivatives of ML potential (simulation-energy-conserving MD) 30,31 or with forces directly predicted by ML (simulation-energy non-conserving MD) 10 . and choose an appropriate affordable model and simulation strategy (Figure 4).…”

“…8,9 It also provides us with a consistent way of estimating atomistic models which do not provide energies, e.g., for ML models which only predict forces but no energies 10 and for novel models which directly predict nuclear coordinates evolution by evaluating neither energies nor forces. 11 Before we move on to pure ML models, we highlight general considerations applicable to any model, either QM or ML. We start by providing a concrete example where simulationenergy conservation does not by itself ensure that the dynamics is of satisfactory quality.…”