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Maho Nakata

Publications and source records attributed to Maho Nakata.

16 recordsLinked to original sources

Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials

Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry optimization. While these geometries do not consistently reach DFT-level chemical accuracy or convergence, they can still improve downstream performance compared to non-relaxed structures. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molecular geometries that benefit property predictions. Our code is publicly available at: https://github.com/divelab/AIRS/

physics.chem-ph

Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations

$\rm{SO}(3)$-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of $\rm{SO}(3)$-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the $\mathcal{O}(L^3)$ CG paths into a single shared parameter set without compromising equivariance, where $L$ is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^4)$. We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (\href{https://github.com/divelab/AIRS/tree/main/OpenMol/TDN}{https://github.com/divelab/AIRS/}).

cs.LG

A Benchmark for Quantum Chemistry Relaxations via Machine Learning Interatomic Potentials

Computational quantum chemistry plays a critical role in drug discovery, chemical synthesis, and materials science. While first-principles methods, such as density functional theory (DFT), provide high accuracy in modeling electronic structures and predicting molecular properties, they are computationally expensive. Machine learning interatomic potentials (MLIPs) have emerged as promising surrogate models that aim to achieve DFT-level accuracy while enabling efficient large-scale atomistic simulations. The development of accurate and transferable MLIPs requires large-scale, high-quality datasets with both energy and force labels. Critically, MLIPs must generalize not only to stable geometries but also to intermediate, non-equilibrium conformations encountered during atomistic simulations. In this work, we introduce PubChemQCR, a large-scale dataset of molecular relaxation trajectories curated from the raw geometry optimization outputs of the PubChemQC project. PubChemQCR is the largest publicly available dataset of DFT-based relaxation trajectories for small organic molecules, comprising approximately 3.5 million trajectories and over 300 million molecular conformations computed at various levels of theory. Each conformation is labeled with both total energy and atomic forces, making the dataset suitable for training and evaluating MLIPs. To provide baselines for future developments, we benchmark nine representative MLIP models on the dataset. Our resources are publicly available at https://huggingface.co/divelab

q-bio.QM

Evaluation of POSIT Arithmetic with Accelerators

We present an evaluation of 32-bit POSIT arithmetic through its implementation as accelerators on FPGAs and GPUs. POSIT, a floating-point number format, adaptively changes the size of its fractional part. We developed hardware designs for FPGAs and software for GPUs to accelerate linear algebra operations using Posit(32,2) arithmetic. Our FPGA- and GPU-based accelerators in Posit(32,2) arithmetic significantly accelerated the Cholesky and LU decomposition algorithms for dense matrices. In terms of numerical accuracy, Posit(32,2) arithmetic is approximately 0.5 - 1.0 digits more accurate than the standard 32-bit format, especially when the norm of the elements of the input matrix is close to 1. Evaluating power consumption, we observed that the power efficiency of the accelerators ranged between 0.043 - 0.076 Gflops/watts for the LU decomposition in Posit(32,2) arithmetic. The power efficiency of the latest GPUs as accelerators of Posit(32,2) arithmetic is better than that of the evaluated FPGA chip.

cs.DC

Accelerating 128-bit Floating-Point Matrix Multiplication on FPGAs

General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application is semidefinite programming (SDP), and it often requires binary128 or higher precision arithmetic to solve problems involving SDP stably. However, only some processors support binary128 arithmetic, which makes SDP solvers generally slow. In this study, we focused on accelerating GEMM with binary128 arithmetic on field-programmable gate arrays (FPGAs) to enable the flexible design of accelerators for the desired computations. Our binary128 GEMM designs on a recent high-performance FPGA achieved approximately 90GFlops, 147x faster than the computation executed on a recent CPU with 20 threads for large matrices. Using our binary128 GEMM design on the FPGA, we successfully accelerated two numerical applications: LU decomposition and SDP problems, for the first time.

cs.DC

PubChemQC B3LYP/6-31G*//PM6 dataset: the Electronic Structures of 86 Million Molecules using B3LYP/6-31G* calculations

This article presents the "PubChemQC B3LYP/6-31G*//PM6" dataset, containing electronic properties of 85,938,443 molecules. It includes orbitals, orbital energies, total energies, dipole moments, and other relevant properties. The dataset encompasses a wide range of molecules, from essential compounds to biomolecules up to 1000 molecular weight, covering 94.0% of the original PubChem Compound catalog (as of August 29, 2016). The electronic properties were calculated using the B3LYP/6-31G* and PM6 methods. The dataset is available in three formats: (i) GAMESS quantum chemistry program files, (ii) selected JSON output files, and (iii) a PostgreSQL database, enabling researchers to query molecular properties. Five sub-datasets offer more specific data. The first two subsets include molecules with C, H, O, and N, under 300 and 500 molecular weight respectively. The third and fourth subsets contain C, H, N, O, P, S, F, and Cl, under 300 and 500 molecular weight respectively. The fifth subset includes C, H, N, O, P, S, F, Cl, Na, K, Mg, and Ca, under 500 molecular weight. Coefficients of determination ranged from 0.892 (CHON500) to 0.803 (whole) for the HOMO-LUMO energy gap. These findings represent extensive investigations and can be utilized for drug discovery, material science, and other applications. The datasets are available under the Creative Commons Attribution 4.0 International license at https://nakatamaho.riken.jp/pubchemqc.riken.jp/b3lyp_pm6_datasets.html.

physics.chem-ph

3D Molecular Geometry Analysis with 2D Graphs

Ground-state 3D geometries of molecules are essential for many molecular analysis tasks. Modern quantum mechanical methods can compute accurate 3D geometries but are computationally prohibitive. Currently, an efficient alternative to computing ground-state 3D molecular geometries from 2D graphs is lacking. Here, we propose a novel deep learning framework to predict 3D geometries from molecular graphs. To this end, we develop an equilibrium message passing neural network (EMPNN) to better capture ground-state geometries from molecular graphs. To provide a testbed for 3D molecular geometry analysis, we develop a benchmark that includes a large-scale molecular geometry dataset, data splits, and evaluation protocols. Experimental results show that EMPNN can efficiently predict more accurate ground-state 3D geometries than RDKit and other deep learning methods. Results also show that the proposed framework outperforms self-supervised learning methods on property prediction tasks.

physics.chem-ph

MPLAPACK version 2.0.1 user manual

The MPLAPACK (formerly MPACK) is a multiple-precision version of LAPACK (https://www.netlib.org/lapack/). MPLAPACK version 2.0.1 is based on LAPACK version 3.9.1 and translated from Fortran 90 to C++ using FABLE, a Fortran to C++ source-to-source conversion tool (https://github.com/cctbx/cctbx_project/tree/master/fable/). MPLAPACK version 2.0.1 provides the real and complex version of MPBLAS, and the real and complex versions of MPLAPACK support all LAPACK features: solvers for systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems, and related matrix factorizations except for mixed-precision routines. The MPLAPACK defines an API for numerical linear algebra, similar to LAPACK. It is easy to port legacy C/C++ numerical codes using MPLAPACK. MPLAPACK supports binary64, binary128, FP80 (extended double), MPFR, GMP, and QD libraries (double-double and quad-double). Users can choose MPFR or GMP for arbitrary accurate calculations, double-double or quad-double for fast 32 or 64-decimal calculations. We can consider the binary64 version as the C++ version of LAPACK. Moreover, it comes with an OpenMP accelerated version of MPBLAS for some routines and CUDA (A100 and V100 support) for double-double versions of Rgemm and Rsyrk. The peak performances of the OpenMP version are almost proportional to the number of cores, and the performances of the CUDA version are impressive, and approximately 400-600 GFlops. MPLAPACK is available at GitHub (https://github.com/nakatamaho/mplapack/) under the 2-clause BSD license.

cs.MS

OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs

Enabling effective and efficient machine learning (ML) over large-scale graph data (e.g., graphs with billions of edges) can have a great impact on both industrial and scientific applications. However, existing efforts to advance large-scale graph ML have been largely limited by the lack of a suitable public benchmark. Here we present OGB Large-Scale Challenge (OGB-LSC), a collection of three real-world datasets for facilitating the advancements in large-scale graph ML. The OGB-LSC datasets are orders of magnitude larger than existing ones, covering three core graph learning tasks -- link prediction, graph regression, and node classification. Furthermore, we provide dedicated baseline experiments, scaling up expressive graph ML models to the massive datasets. We show that expressive models significantly outperform simple scalable baselines, indicating an opportunity for dedicated efforts to further improve graph ML at scale. Moreover, OGB-LSC datasets were deployed at ACM KDD Cup 2021 and attracted more than 500 team registrations globally, during which significant performance improvements were made by a variety of innovative techniques. We summarize the common techniques used by the winning solutions and highlight the current best practices in large-scale graph ML. Finally, we describe how we have updated the datasets after the KDD Cup to further facilitate research advances. The OGB-LSC datasets, baseline code, and all the information about the KDD Cup are available at https://ogb.stanford.edu/docs/lsc/ .

cs.LG

Molecule3D: A Benchmark for Predicting 3D Geometries from Molecular Graphs

Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing of 3D molecular geometries requires quantum calculations that are computationally prohibitive. For example, accurate calculation of 3D geometries of a small molecule requires hours of computing time using density functional theory (DFT). Here, we propose to predict the ground-state 3D geometries from molecular graphs using machine learning methods. To make this feasible, we develop a benchmark, known as Molecule3D, that includes a dataset with precise ground-state geometries of approximately 4 million molecules derived from DFT. We also provide a set of software tools for data processing, splitting, training, and evaluation, etc. Specifically, we propose to assess the error and validity of predicted geometries using four metrics. We implement two baseline methods that either predict the pairwise distance between atoms or atom coordinates in 3D space. Experimental results show that, compared with generating 3D geometries with RDKit, our method can achieve comparable prediction accuracy but with much smaller computational costs. Our Molecule3D is available as a module of the MoleculeX software library (https://github.com/divelab/MoleculeX).

cs.LG

White Paper from Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing

In numerical computations, precision of floating-point computations is a key factor to determine the performance (speed and energy-efficiency) as well as the reliability (accuracy and reproducibility). However, precision generally plays a contrary role for both. Therefore, the ultimate concept for maximizing both at the same time is the minimal-precision computing through precision-tuning, which adjusts the optimal precision for each operation and data. Several studies have been already conducted for it so far (e.g. Precimoniuos and Verrou), but the scope of those studies is limited to the precision-tuning alone. Hence, we aim to propose a broader concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. In 2019, we have started the Minimal-Precision Computing project to propose a more broad concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. Specifically, our system combines (1) a precision-tuning method based on Discrete Stochastic Arithmetic (DSA), (2) arbitrary-precision arithmetic libraries, (3) fast and accurate numerical libraries, and (4) Field-Programmable Gate Array (FPGA) with High-Level Synthesis (HLS). In this white paper, we aim to provide an overview of various technologies related to minimal- and mixed-precision, to outline the future direction of the project, as well as to discuss current challenges together with our project members and guest speakers at the LSPANC 2020 workshop; https://www.r-ccs.riken.jp/labs/lpnctrt/lspanc2020jan/.

cs.DC

PubChemQC PM6: A dataset of 221 million molecules with optimized molecular geometries and electronic properties

We report on the largest dataset of optimized molecular geometries and electronic properties calculated by the PM6 method for 92.9% of the 91.2 million molecules cataloged in PubChem Compounds retrieved on Aug. 29, 2016. In addition to neutral states, we also calculated those for cationic, anionic, and spin flipped electronic states of 56.2%, 49.7%, and 41.3% of the molecules, respectively. Thus, the grand total calculated is 221 million molecules. The dataset is available at http://pubchemqc.riken.jp/pm6_dataset.html under the Creative Commons Attribution 4.0 International license.

physics.chem-ph

The PubChemQC Project: a large chemical database from the first principle calculations

In this research, we have been constructing a large database of molecules by {\it ab initio} calculations. Currently, we have over 1.53 million entries of 6-31G* B3LYP optimized geometries and ten excited states by 6-31+G* TDDFT calculations. To calculate molecules, we only refer the InChI (International Chemical Identifier) representation of chemical formula by the International Union of Pure and Applied Chemistry (IUPAC), thus, no reference to experimental data. These results are open to public at http://pubchemqc.riken.jp/. The molecular data have been taken from the PubChem Project (http://pubchem.ncbi.nlm.nih.gov/) which is one of the largest in the world (approximately 63 million molecules are listed) and free (public domain) database. Our final goal is, using these data, to develop a molecular search engine or molecular expert system to find molecules which have desired properties.

physics.chem-ph

The second-order reduced density matrix method and the two-dimensional Hubbard model

The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T)) accuracy without using the wave-function. One question that arises is how well does the RDM method perform with the same conditions that result in CCSD(T) accuracy in the strong correlation limit. The simplest and a theoretically important model for strongly correlated electronic systems is the Hubbard model. In this paper, we establish the utility of the RDM method when employing the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions in the two-dimension al Hubbard model case and we conduct a thorough study applying the $4\times 4$ Hubbard model employing a coefficients. Within the Hubbard Hamilt onian we found that even in the intermediate setting, where $U/t$ is between 4 and 10, the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions re produced good ground state energies.

cond-mat.str-el

On the size-consistency of the reduced-density-matrix method and the unitary invariant diagonal $N$-representability conditions

Variational calculation of the ground state energy and its properties using the second-order reduced density matrix (2-RDM) is a promising approach for quantum chemistry. A major obstacle with this approach is that the $N$-representability conditions are too difficult in general. Therefore, we usually employ some approximations such as the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions, for realistic calculations. The results of using these approximations and conditions in 2-RDM are comparable to those of CCSD(T). However, these conditions do not incorporate an important property; size-consistency. Size-consistency requires that energies $E(A)$, $E(B)$ and $E(A...B)$ for two infinitely separated systems $A$, $B$, and their respective combined system $A...B$, to satisfy $E(A...B) = E(A) + E(B)$. In this study, we show that the size-consistency can be satisfied if 2-RDM satisfies the following conditions: (i) 2-RDM is unitary invariant diagonal $N$-representable; (ii) 2-RDM corresponding to each subsystem is the eigenstate of the number of corresponding electrons; and (iii) 2-RDM satisfies at least one of the $ P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions.

physics.chem-ph

Variational approach for the electronic structure calculation on the second-order reduced density matrices and the $N$-representability problem

The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schrödinger equation for the ground state. The number of variables is the same as a four electron system and constant regardless of the electrons in the system. Thus many researchers have been dreaming of a much simpler method for quantum mechanics. In this chapter, we give a overview of the reduced-density matrix method; details of the theories, methods, history, and some new computational results. Typically, the results are comparable to the CCSD(T) which is a sophisticated traditional approach in quantum chemistry.

cond-mat.str-el