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.

For decades, supercritical flame simulations incorporating detailed chemistry and real-fluid transport have been limited to millions of cells, constraining the resolved spatial and temporal scales of the physical system. We optimize the supercritical flame simulation software DeepFlame—which incorporates deep neural networks while retaining the real-fluid mechanical and chemical accuracy—from three perspectives: parallel computing, computational efficiency, and I/O performance. Our highly optimized DeepFlame achieves supercritical liquid oxygen/methane (LOX/\(\ce {CH4}\)) turbulent combustion simulation of up to 618 and 154 billion cells with unprecedented time-to-solution, attaining 439/1186 and 187/316 PFlop/s (32.3%/21.8% and 37.4%/31.8% of the peak) in FP32/mixed-FP16 precision on Sunway (98,304 nodes) and Fugaku (73,728 nodes) supercomputers, respectively. This computational capability surpasses existing capacities by three orders of magnitude, enabling the first practical simulation of rocket engine combustion with >100 LOX/\(\ce {CH4}\) injectors. This breakthrough establishes high-fidelity supercritical flame modeling as a critical design tool for next-generation rocket propulsion and ultra-high energy density systems.

Physical phenomena such as bond breaking and phase transitions require molecular dynamics (MD) withab initioaccuracy, involving up to billions of atoms and over nanosecond timescales. Previous state-of-the-art work has demonstrated that neural network molecular dynamics (NNMD) like deep potential molecular dynamics (DeePMD), can successfully extend the temporal and spatial scales of MD withab initioaccuracy on both ARM and GPU platforms. However, the DeePMD-kit package is currently unable to fully exploit the computational potential of the new Sunway supercomputer due to its unique many-core architecture, memory hierarchy, and low precision capability. In this paper, we re-design the DeePMD-kit to harness the massive computing power of the new Sunway, enabling the MD with over ten billion atoms. We first design a large-scale parallelization scheme to exploit the massive parallelism of the new Sunway. Then we devise specialized optimizations for the time-consuming operators. Finally, we design a novel mixed precision method for DeePMD-kit customized operators to leverage the low precision computing power of the new Sunway. The optimized DeePMD-kit achieves 67.6 / 56.5$\boldsymbol{\times}$speedup for water / copper systems on the new Sunway. Meanwhile, it can perform 29 billion atoms simulation for the water system on 35 million cores (i.e., 90,000 computing nodes, around 84% of the whole supercomputer) with a peak performance of 57.1 PFLOPs, which is 7.9$\boldsymbol{\times}$bigger and 1.2$\boldsymbol{\times}$faster than state-of-the-art results. This paves the way for investigating more realistic scenarios, such as studying the mechanical properties of metals, semiconductor devices, batteries, and other materials and physical systems.

Physical phenomena such as chemical reactions, bond breaking, and phase transition require molecular dynamics (MD) simulation with ab initio accuracy ranging from milliseconds to microseconds. However, previous state-of-the-art neural network based MD packages such as DeePMD-kit can only reach 4.7 nanoseconds per day on the Fugaku supercomputer. In this paper, we present a novel node-based parallelization scheme to reduce communication by 81%, then optimize the computationally intensive kernels with sve-gemm and mixed precision. Finally, we implement intra-node load balance to further improve the scalability. Numerical results on the Fugaku supercomputer show that our work has significantly improved the time-to-solution of the DeePMD-kit by a factor of 31.7 x, reaching 149 nanoseconds per day on 12,000 computing nodes. This work has opened the door for millisecond simulation with ab initio accuracy within one week for the first time.

Physical phenomenon such as protein folding requires simulation up to microseconds of physical time, which directly corresponds to the strong scaling of molecular dynamics(MD) on modern supercomputers. In this paper, we present a highly scalable implementation of the state-of-the-art MD code LAMMPS on Fugaku by exploiting the 6D mesh/torus topology of the TofuD network. Based on our detailed analysis of the MD communication pattern, we first adapt coarse-grained peer-to-peer ghost-region communication with uTofu interface, then further improve the scalability via fine-grained thread pool. Finally, Remote direct memory access (RDMA) primitives are utilized to avoid buffer overhead. Numerical results show that our optimized code can reduce 77% of the communication time, improving the performance of baseline LAMMPS by a factor of 2.9x and 2.2x for Lennard-Jones and embedded-atom method potentials when scaling to 36, 846 computing nodes. Our optimization techniques can also benefit other applications with stencil or domain decomposition methods.

High-performance computing, together with a neural network model trained from data generated with first-principles methods, has greatly boosted applications of ab initio molecular dynamics in terms of spatial and temporal scales on modern supercomputers. Previous state-of-the-art can achieve 1 -- 2 nanoseconds molecular dynamics simulation per day for 100-million atoms on the entire Summit supercomputer. In this paper, we have significantly reduced the memory footprint and computational time by a comprehensive approach with both algorithmic and system innovations. The neural network model is compressed by model tabulation, kernel fusion, and redundancy removal. Then optimizations such as acceleration of customized kernel, tabulation of activation function, MPI+OpenMP parallelization are implemented on GPU and ARM architectures. Testing results of the copper system show that the optimized code can scale up to the entire machine of both Fugaku and Summit, and the corresponding system size can be extended by a factor of 134 to an unprecedented 17 billion atoms. The strong scaling of a 13.5-million atom copper system shows that the time-to-solution can be 7 times faster, reaching 11.2 nanoseconds per day. This work opens the door for unprecedentedly large-scale molecular dynamics simulations based on ab initio accuracy and can be potentially utilized in studying more realistic applications such as mechanical properties of metals, semiconductor devices, batteries, etc. The optimization techniques detailed in this paper also provide insight for relevant high-performance computing applications.

Over the past three decades, ab initio electronic structure calculations of large, complex and metallic systems are limited to tens of thousands of atoms in computational accuracy and efficiency on leadership supercomputers. We present a massively parallel discontinuous Galerkin density functional theory (DGDFT) implementation, which adopts adaptive local basis functions to discretize the Kohn-Sham equation, resulting in a block-sparse Hamiltonian matrix. A highly efficient pole expansion and selected inversion (PEXSI) sparse direct solver is implemented in DGDFT to achieve O(N1.5) scaling for quasi two-dimensional systems. DGDFT allows us to compute the electronic structures of complex metallic heterostructures with 2.5 million atoms (17.2 million electrons) using 35.9 million cores on the new Sunway supercomputer. The peak performance of PEXSI can achieve 64 PFLOPS (~5% of theoretical peak), which is un-precedented for sparse direct solvers. This accomplishment paves the way for quantum mechanical simulations into mesoscopic scale for designing next-generation electronic devices.