Ultra-fast electronic phenomena originating from finite temperature, such as nonlinear optical excitation, can be simulated with high fidelity via real-time time dependent density functional theory (rt-TDDFT) calculations with hybrid functional. However, previous rt-TDDFT simulations of real materials using the optimal gauge-known as the parallel transport gauge-have been limited to low-temperature systems with band gaps. In this paper, we introduce the parallel transport-implicit midpoint (PT-IM) method, which significantly accelerates finitetemperature rt-TDDFT calculations of real materials with hybrid function. We first implement PT-IM with hybrid functional in our plane wave code PWDFT, and optimized it on both GPU and ARM platforms to build a solid baseline code. Next, we propose a diagonalization method to reduce computation and communication complexity, and then, we employ adaptively compressed exchange (ACE) method to reduce the frequency of the most expensive Fock exchange operator. Finally, we adopt the ring_based method and the shared memory mechanism to overlap computation and communication and alleviate memory consumption respectively. Numerical results show that our optimized code can reach 3072 atoms for rt-TDDFT simulation with hybrid functional at finite temperature on 192 computing nodes, the time-to-solution for one time step is 429.3 s, which is 41.4 times faster compared to the baseline.

Neural Network Molecular Dynamics (NNMD) has become a major approach in material simulations, which can speedup the molecular dynamics (MD) simulation for thousands of times, while maintaining ab initio accuracy, thus has a potential to fundamentally change the paradigm of material simulations. However, there are two time-consuming bottlenecks of the NNMD developments. One is the data access of ab initio calculation results. The other, which is the focus of the current work, is reducing the training time of NNMD model. The training of NNMD model is different from most other neural network training because the atomic force (which is related to the gradient of the network) is an important physical property to be fit. Tests show the traditional stochastic gradient methods, like the Adam algorithms, cannot efficiently deploy the multisample minibatch algorithm. As a result, a typical training (taking the Deep Potential Molecular Dynamics (DeePMD) as an example) can take many hours. In this work, we designed a heuristic minibatch quasi-Newtonian optimizer based on Extended Kalman Filter method. An early reduction of gradient and error is adopted to reduce memory footprint and communication. The memory footprint, communication and settings of hyper-parameters of this new method are analyzed in detail. Computational innovations such as customized kernels of the symmetry-preserving descriptor are applied to exploit the computing power of the heterogeneous architecture. Experiments are performed on 8 different datasets representing different real case situations, and numerical results show that our new method has an average speedup of 32.2 compared to the Reorganized Layer-wised Extended Kalman Filter with 1 GPU, reducing the absolute training time of one DeePMD model from hours to several minutes, making it one step toward online training.

It is imperative to accelerate the training of neural network force field such as Deep Potential, which usually requires thousands of images based on first-principles calculation and a couple of days to generate an accurate potential energy surface. To this end, we propose a novel optimizer named reorganized layer extended Kalman filtering (RLEKF), an optimized version of global extended Kalman filtering (GEKF) with a strategy of splitting big and gathering small layers to overcome the O(N^2) computational cost of GEKF. This strategy provides an approximation of the dense weights error covariance matrix with a sparse diagonal block matrix for GEKF. We implement both RLEKF and the baseline Adam in our alphaDynamics package and numerical experiments are performed on 13 unbiased datasets. Overall, RLEKF converges faster with slightly better accuracy. For example, a test on a typical system, bulk copper, shows that RLEKF converges faster by both the number of training epochs (x11.67) and wall-clock time (x1.19). Besides, we theoretically prove that the updates of weights converge and thus are against the gradient exploding problem. Experimental results verify that RLEKF is not sensitive to the initialization of weights. The RLEKF sheds light on other AI-for-science applications where training a large neural network (with tons of thousands parameters) is a bottleneck.