In this work we present nablaDFT, the new dataset and benchmark for the Density Functional Theory Hamiltonian and energy prediction. We provide data for over 1 million different molecules and over 5 million conformations and baseline models for both tasks.

Additive manufacturing is a modern technique to produce parts with a complex geometry. However, the choice of the printing parameters is a time-consuming and costly process. In this study, the parameter optimization for the laser powder bed fusion process was investigated. Using state-of-the art multi-objective Bayesian optimization, the set of the most-promising process parameters (laser power, scanning speed, hatch distance, etc.), which would yield parts with the desired hardness and porosity, was established. The Gaussian process surrogate model was built on 57 empirical data points, and through efficient sampling in the design space, we were able to obtain three points in the Pareto front in just over six iterations. The produced parts had a hardness ranging from 224–235 HV and a porosity in the range of 0.2–0.37%. The trained model recommended using the following parameters for high-quality parts: 58 W, 257 mm/s, 45 µm, with a scan rotation angle of 131 degrees. The proposed methodology greatly reduces the number of experiments, thus saving time and resources. The candidate process parameters prescribed by the model were experimentally validated and tested.

Kirkpatrick et al . (Reports, 9 December 2021, p. 1385) trained a neural network–based DFT functional, DM21, on fractional-charge (FC) and fractional-spin (FS) systems, and they claim that it has outstanding accuracy for chemical systems exhibiting strong correlation. Here, we show that the ability of DM21 to generalize the behavior of such systems does not follow from the published results and requires revisiting.

Density functional theory is the workhorse of present-day quantum chemistry thanks to its good balance between calculation accuracy and speed. In recent years, several neural network-based exchange–correlation functionals have been developed, with DM21, developed by Google DeepMind, being the most recognizable among them. In this study, we focus on evaluating the efficiency of DM21 functional on the task of optimizing molecular geometries and investigate how the non-smooth behavior of neural network-predicted exchange–correlation energy and potential affects the final geometry precision. We implement geometry optimization for the DM21 functional in PySCF and compare its performance with traditional functionals on various benchmarks. Our findings reveal that numerical noise coming from the neural network outputs contaminates numerical nuclear gradients required for geometry optimization. We also found that a numerical differentiation step in the range of 0.0001–0.001 Å is required to obtain sufficiently smooth nuclear gradients. Furthermore, we show that the non-smoothness of DM21 can be reproduced by adding random normally distributed noise to local energies of an analytical SCAN functional, allowing one to efficiently estimate the optimal numerical differentiation step for geometry optimization of a given molecule. Our findings show that DM21 does not outperform analytical functionals in the accuracy of optimized molecular geometries and is significantly slower, which limits its practical applicability to chemical calculations.

Efficient simulations of complex physical systems described by partial differential equations (PDE) require computational methods that can reduce the resource demands without sacrificing the accuracy. Here, we introduce a framework based on graph neural networks (GNN) for learnable self-supervised differentiable coarsening of unstructured computational grids. We leverage graph-based representation of the physical system and offer a computational grid coarsening method which preserves the underlying physical properties together with the stability of the chosen numerical scheme with the help of the designed loss terms. The coarsening model is trained in a self-supervised way by minimizing the error between the output of the simulations on the coarsened and original grids.We evaluate the approach on four PDE systems of different types, covering both linear and nonlinear regimes, including subsurface flow and wave propagation. We demonstrate that the proposed framework exhibits the ability to maintain high fidelity in simulation outputs even after 95% reduction in the number of nodes, significantly reducing computational overhead. We show that the model exhibits generalizability to unseen scenarios, thereby outperforming the baselines. The generality of the developed framework is also proven by its possibility to adapt to implicit numerical schemes used to model stiff systems of PDEs. Thus, the developed approach demonstrates the ability to accelerate physical simulations without compromising accuracy.

Due to the high computational load of modern numerical simulation, there is a demand for approaches that would reduce the size of discrete problems while keeping the accuracy reasonable. In this work, we present an original algorithm to coarsen an unstructured grid based on the concepts of differentiable physics. We achieve this by employing k-means clustering, autodifferentiation and stochastic minimization algorithms. We demonstrate performance of the designed algorithm on two PDEs: a linear parabolic equation which governs slightly compressible fluid flow in porous media and the wave equation. Our results show that in the considered scenarios, we reduced the number of grid points up to 10 times while preserving the modeled variable dynamics in the points of interest. The proposed approach can be applied to the simulation of an arbitrary system described by evolutionary partial differential equations.