[1] [1] HOHENBERG P, KOHN W J P r. Inhomogeneous electron gas[J]. Phys Rev, 1964, 136(3B): B864?871.

[2] [2] CAR R, PARRINELLO M. Unified approach for molecular dynamics and density-functional theory[J]. Phys Rev Lett, 1985, 55(22): 2471?2474.

[3] [3] ZHAO Y, TRUHLAR D G. Density Functionals with Broad Applicability in Chemistry[J]. Account Chem Res, 2008, 41(2): 157?167.

[4] [4] ROUSSEA A, SELLONI A. Theoretical insights into the surface physics and chemistry of redox-active oxides[J]. Nat Rev Mater, 2020, 5(6): 460?475.

[5] [5] JORDAN M I, MITCHELL T M. Machine learning: Trends, perspectives, and prospects[J]. Science, 2015, 349(6245): 255?260.

[6] [6] BLANK T B, BROWN S D, CALHOUN A W, et al. Neural-Network Models of Potential-Energy Surfaces[J]. J Chem Phys, 1995, 103(10): 4129?4137.

[7] [7] LIU T, FU B, ZHANG D H. Six-dimensional quantum dynamics study for the dissociative adsorption of HCl on Au(111) surface[J]. J Chem Phys, 2013, 139(18): 184705

[8] [8] BEHLER J, PARRINELLO M. Generalized neural-network representation of high-dimensional potential-energy surfaces[J]. Phys Rev Lett, 2007, 98(14): 146401.

[9] [9] BEHLER J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials[J]. J Chem Phys, 2011, 134(7): 074106.

[10] [10] SOSSO G C, MICELI G, CARAVATI S, et al. Neural network interatomic potential for the phase change material GeTe[J]. Phys Rev B, 2012, 85(17): 174103.

[11] [11] RUPP M, TKATCHENKO A, MULLER K R, et al. Fast and accurate modeling of molecular atomization energies with machine learning[J]. Phys Rev Lett, 2012, 108(5): 058301.

[12] [12] BART?K A P, KONDOR R, CS?NYI G. On representing chemical environments[J]. Phys Rev B, 2013, 87(18): 184115.

[13] [13] KERMOD L R, DE VITA A. Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces[J]. Phys Rev Lett, 2015, 114(9): 096405.

[14] [14] BART?K A P, CS?NYI G. Gaussian approximation potentials: A brief tutorial introduction[J]. Int J Quantum Chem, 2015, 115(16): 1051?1057.

[15] [15] BEHLER J. Perspective: Machine learning potentials for atomistic simulations[J]. J Chem Phys, 2016, 145(17): 170901.

[16] [16] KOLB B, ZHAO B, LI J, et al. Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks[J]. J Chem Phys, 2016, 144(22): 224103.

[17] [17] DE S, BARTOK A P, CSANYI G, et al. Comparing molecules and solids across structural and alchemical space[J]. Phys Chem Chem Phys, 2016, 18(20): 13754?13769.

[18] [18] SMITH J S, ISAYEV O, ROITBERG A E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost[J]. Chem Sci, 2017, 8(4): 3192?3203.

[19] [19] SCHUTT K T, ARBABZADAH F, CHMIELA S, et al. Quantum-chemical insights from deep tensor neural networks[J]. Nat Commun, 2017, 8: 13890.

[20] [20] HUANG S D, SHANG C, ZHANG X-J, et al. Material discovery by combining stochastic surface walking global optimization with a neural network[J]. Chem Sci, 2017, 8(9): 6327?6337.

[21] [21] HUANG S D, SHANG C, KANG P-L, et al. Atomic structure of boron resolved using machine learning and global sampling[J]. Chem Sci, 2018, 9(46): 8644?8655.

[22] [22] J?GER M O J, MOROOKA E V, FEDERICI CANOVA F, et al. Machine learning hydrogen adsorption on nanoclusters through structural descriptors[J]. NPJ Comput Mater, 2018, 4(1): 37.

[23] [23] SCHUTT K T, SAUCEDA H E, KINDERMANS P J, et al. SchNet-A deep learning architecture for molecules and materials[J]. J Chem Phys, 2018, 148(24): 241722.

[24] [24] ZHANG L, HAN J, WANG H, et al. Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics[J]. Phys Rev Lett, 2018, 120(14): 143001.

[25] [25] JACOBSEN T L, JORGENSEN M S, HAMMER B. On-the-fly machine learning of atomic potential in density functional theory structure optimization[J]. Phys Rev Lett, 2018, 120(2): 026102.

[26] [26] TONG Q, XUE L, LV J, et al. Accelerating CALYPSO structure prediction by data-driven learning of a potential energy surface[J]. Faraday Discuss, 2018, 211, 31?43.

[27] [27] HUANG S D, SHANG C, KANG P L, et al. LASP: Fast global potential energy surface exploration[J]. WIRES Comput Mol Sci, 2019, 9(6): e1415.

[28] [28] FRIEDERICHP, H?SE F, PROPPE J. et al. Machine-learned potentials for next-generation matter simulations, Nature Materials, 2021, 20(6), 750?761.

[29] [29] JINNOUCHI R, MIWA K, KARSAI F, et al. On-the-fly active learning of interatomic potentials for large-scale atomistic simulations[J]. J Phys Chem Lett, 2020, 11(17): 6946?6955.

[30] [30] COHN D A, GHAHRAMANI Z, JORDAN M I. Active learning with statistical models[J]. J. Artif Int Res, 1996, 4(1): 129-145.

[31] [31] TRUHLAR D G, GORDON M S. From force fields to dynamics: Classical and quantal paths[J]. Science, 1990, 249(4968): 491?498.

[32] [32] CARO M A, DERINGER V L, KOSKINEN J, et al. Growth mechanism and origin of high sp3 content in tetrahedral amorphous carbon[J]. Phys Res Lett, 2018, 120(16): 166101.

[33] [33] MOCANU F C, KONSTANTINOU K, LEE T H, et al. Modeling the phase-change memory material, Ge2Sb2Te5, with a machine-learned interatomic potential[J]. J Phys Chem B, 2018, 122(38): 8998?9006.

[34] [34] BALABIN R M, LOMAKINA E I. Support vector machine regression (LS-SVM)-an alternative to artificial neural networks (ANNs) for the analysis of quantum chemistry data?[J]. Phys Chem Chem Phys, 2011, 13(24): 11710?11718.

[35] [35] ELAHE A, HOOMAN A, DAVOOD I. Experimental investigation and development of a SVM model for hydrogenation reaction of carbon monoxide in presence of Co-Mo/Al2O3 catalyst[J]. Chem Eng J, 2015, 276: 213?221.

[36] [36] THOMPSON A P, SWILER L P, TROTT C R, et al. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials[J]. J Comput Phys, 2015, 285: 316?330.

[37] [37] ZHANG L F, HAN J Q, WANG H, et al. Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics[J]. Phys Rev Lett, 2018, 120(14): 143001.

[38] [38] HAN J, ZHANG L, CAR R, et al. Deep potential: A general representation of a many-body potential energy surface[J]. Commun Comput Phys, 2018, 23(3): 629?639.

[39] [39] SANCHEZ-LENGELING B, REIF E, PEARCE A, et al. A gentle introduction to graph neural networks[J]. Distill, 2021, 6: e33.

[40] [40] SCH?TT K T, ARBABZADAH F, CHMIELA S, et al. Quantum- chemical insights from deep tensor neural networks[J]. Nat Commun, 2017, 8: 13890.

[41] [41] SCHUTT K, KINDERMANS P, SAUCEDA H, et al. SchNet: A continuous-filter convolutional neural network for modeling quantum interactions//Advances in Neural Information Processing Systems[M]. Curran Associates, Inc., 2017; Vol. 30.

[42] [42] ZHANG Y, HU C, JIANG B. Embedded atom neural network potentials: Efficient and accurate machine learning with a physically inspired representation[J]. J Phys Chem Lett, 2019, 10(17): 4962?4967.

[43] [43] LIU Y, GUO B, ZOU X, et al. Machine learning assisted materials design and discovery for rechargeable batteries[J]. Energy Storage Mater, 2020, 31: 434?450.

[44] [44] LIU Y, ZOU X, YANG Z, et al. Machine Learning Embedded with Materials Domain Knowledge[J]. J Chin Ceram Soc, 2022, 50(3): 863?876.

[45] [45] KOCER E, KO T W, BEHLER J. Neural network potentials: A concise overview of methods[J]. Annual Rev Phys Chem, 2022, 73(1): 163?186.

[46] [46] UNKE O T, CHMIELA S, SAUCEDA H E, et al. Machine learning force fields[J]. Chem Rev, 2021, 121(16): 10142?10186.

[47] [47] KANG P L, SHANG C, LIU Z P. Large-scale atomic simulation via machine learning potentials constructed by global potential energy surface exploration[J]. Account Chem Res, 2020, 53(10): 2119?2129.

[48] [48] GHASEMI S A, HOFSTETTER A, SAHA S, et al. Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network[J]. Phys Rev B Condensed Matter Mater Phys, 2015, 92(4): 045131.

[49] [49] KO T W, FINKLER J A, GOEDECKER S, et al. A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer[J]. Nat Commun, 2021, 12 (1): 398.

[50] [50] FINK T, BRUGGESSER H, REYMOND J L. Virtual exploration of the small-molecule chemical universe below 160 Daltons[J]. Angew Chem Int Ed Engl, 2005, 44(10): 1504?1508.

[51] [51] RUDDIGKEIT L, VAN DEURSEN R, BLUM L C, et al. Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17[J]. J Chem Inform Model, 2012, 52(11): 2864?2875.

[52] [52] RAMAKRISHNAN R, DRAL P O, RUPP M, et al. Quantum chemistry structures and properties of 134 kilo molecules[J]. Sci Data, 2014, 1: 140022.

[53] [53] KIRKPATRICK S, GELATT C D, VECCHI M P. Optimization by simulated annealing[J]. Science, 1983, 220(4598): 671?680.

[54] [54] PANNETIER J, BASSAS-ALSINA J, RODRIGUEZ-CARVAJAL J, et al. Prediction of crystal structures from crystal chemistry rules by simulated annealing[J]. Nature, 1990, 346(6282): 343?345.

[55] [55] SCH?N J C, JANSEN M. First step towards planning of syntheses in solid-state chemistry: Determination of promising structure candidates by global optimization[J]. Angew Chem Int Ed Engl, 1996, 35(12): 1286?1304.

[56] [56] GASTEGGER M, MARQUETAND P. High-dimensional neural network potentials for organic reactions and an improved training algorithm[J]. J Chem Theory Comput, 2015, 11(5): 2187?2198.

[57] [57] HERR J E, YAO K, MCINTYRE R, et al. Metadynamics for training neural network model chemistries: A competitive assessment[J]. J Chem Phys, 2018, 148(24): 241710.

[58] [58] AMABILINO S, BRATHOLM L A, BENNIE S J, et al. Training neural nets to learn reactive potential energy surfaces using interactive quantum chemistry in virtual reality[J]. J Phys Chem A, 2019, 123(20): 4486?4499.

[59] [59] SMIT J S, NEBGEN B, LUBBERS N, et al. Less is more: Sampling chemical space with active learning[J]. J Chem Phys, 2018, 148(24): 241733.

[60] [60] SMITH J S, ZUBATYUK R, NEBGEN B, et al. The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules[J]. Sci Data, 2020, 7(1): 1?10.

[61] [61] WALES D J, DOYE J P K. Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 Atoms[J]. J Phys Chem A, 1997, 101(28): 5111?5116.

[62] [62] ARTRITH N, URBAN A, CEDER G. Constructing first-principles phase diagrams of amorphous LixSi using machine-learning-assisted sampling with an evolutionary algorithm[J]. J Chem Phys, 2018, 148(24): 241711.

[63] [63] GUAN S H, SHANG C, HUANG S-D, et al. Two-stage solid-phase transition of cubic ice to hexagonal ice: Structural origin and kinetics[J]. J Phys Chem C, 2018, 122(50): 29009?29016.

[64] [64] KONG F C, LI Y F, SHANG C, et al. Stability and phase transition of cobalt oxide phases by machine learning global potential energy surface[J]. J Phys Chem C, 2019, 123(28): 17539?17547.

[65] [65] HUANG S D, SHANG C, LIU Z P. Ultrasmall Au clusters supported on pristine and defected CeO2: Structure and stability[J]. J Chem Phys, 2019, 151(17): 174702.

[66] [66] LI Y F, LIU Z P. Active Site revealed for water oxidation on electrochemically induced δ-MnO2: Role of spinel-to-layer phase transition[J]. J Am Chem Soc, 2018, 140(5): 1783?1792.

[67] [67] GUAN S H, ZHANG K X, SHANG C, et al. Stability and anion diffusion kinetics of yttria-stabilized zirconia resolved from machine learning global potential energy surface exploration[J]. J Chem Phys, 2020, 152(9): 094703.

[68] [68] MA S, HUANG S D, LIU Z P. Dynamic coordination of cations and catalytic selectivity on zinc-chromium oxide alloys during syngas conversion[J]. Nat Catal, 2019, 2(8): 671?677.

[69] [69] KANG P L, SHANG C, LIU Z P. Glucose to 5-hydroxymethylfurfural: origin of site-selectivity resolved by machine learning based reaction sampling[J]. J Am Chem So, 2019, 141(51): 20525?20536.

[70] [70] SHANG C, LIU Z P. Stochastic surface walking method for structure prediction and pathway searching[J]. J Chem Theory Comput, 2013, 9(3): 1838?1845.

[71] [71] ZHANG X J, SHANG C, LIU Z P. From atoms to fullerene: Stochastic surface walking solution for automated structure prediction of complex material[J]. J Chem Theory Comput, 2013, 9(7): 3252?3260.

[72] [72] SHANG C, ZHANG X J, LIU Z P. Stochastic surface walking method for crystal structure and phase transition pathway prediction[J]. Phys Chem Chem Phys, 2014, 16(33): 17845?17856.

[73] [73] LAIO A, PARRINELLO M. Escaping free-energy minima[J]. Proceed National Academy Sci United States of America, 2002, 99(20): 12562?12566.

[74] [74] METROPOLIS N, ROSENBLUTH A W, ROSENBLUTH M N, et al. Equation of state calculations by fast computing machines[J]. J Chem Phys, 1953, 21(6): 1087?1092.

[75] [75] ZHAN, SHAN C, LIU Z P. Pressure-induced silica quartz amorphization studied by iterative stochastic surface walking reaction sampling[J]. Phys Chem Chem Phys, 2017, 19(6): 4725?4733.

[76] [76] STEINHARDT P J, NELSON D R, RONCHETTI M. Bond- orientational order in liquids and glasses[J]. Phys Rev B, 1983, 28(2): 784?805.

[77] [77] SETTLES B. Active Learning Literature Survey, Computer Sciences Technical Report 1648[R]. 2009, University of Wisconsin Madison.

[78] [78] TIAN Y, LOOKMAN T, XUE D. Efficient sampling for decision making in materials discovery[J]. Chin Phys B, 2021, 30(5): 050705.

[79] [79] GUAN Y, YANG S, ZHANG D H. Construction of reactive potential energy surfaces with Gaussian process regression: active data selection[J]. Molecul Phys, 2018, 116(7): 823?834.

[80] [80] PODRYABINKIN E V, SHAPEEV A V. Active learning of linearly parametrized interatomic potentials[J]. Comput Mater Sci, 2017, 140: 171?180.

[81] [81] PROPPE J, GUGLER S, REIHER M. Gaussian process-based refinement of dispersion corrections[J]. J Chem Theory Comput, 2019, 15(11): 6046?6060.

[82] [82] TANG Y H, DE JONG W A. Prediction of atomization energy using graph kernel and active learning[J]. J Chem Phys, 2019, 150(4): 044107.

[83] [83] IMBALZANO G, ZHUANG Y, KAPIL V, et al. Uncertainty estimation for molecular dynamics and sampling[J]. J Chem Phys, 2021, 154(7): 074102.

[84] [84] LIN Q, ZHANG Y, ZHAO B, et al. Automatically growing global reactive neural network potential energy surfaces: A trajectory-free active learning strategy[J]. J Chem Phys, 2020, 152(15): 154104.

[85] [85] LIN Q, ZHANG L, ZHANG Y, et al. Searching Configurations in Uncertainty Space: Active Learning of High-Dimensional Neural Network Reactive Potentials[J]. J Chem Theory Comput, 2021, 17(5): 2691?2701.

[86] [86] ZHANG Y, WANG H, CHEN W, et al. DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models[J]. Comput Phys Commun, 2020, 253: 107206.

[87] [87] ZHANG L, LIN D Y, WANG H, et al. Active learning of uniformly accurate interatomic potentials for materials simulation[J]. Phys Rev Mater, 2019, 3(2): 023804.

[88] [88] PENG Y, SHANG C, LIU Z P. The dome of gold nanolized for catalysis[J]. Chem Sci, 2021, 12(15): 5664?5671.

[89] [89] SHANG C, LIU Z P. Chapter 14-Constructing machine learning potentials with active learning, Quantum Chemistry in the Age of Machine Learning, Elsevier, 2023, 313?327.

[90] [90] HUANG S D, SHANG C, KANG P-L, et al. LASP: Fast global potential energy surface exploration[J]. Comput Molecul Sci, 2019, 9: e1415

[91] [91] ECKSTROM H C, ADCOCK W A. A New Iron Carbide in Hydrocarbon Synthesis Catalysts[J]. J Am Chem Soc, 1950, 72(2): 1042?1043.

[92] [92] HOFER L J E, COHN E M, PEEBLES W C. The Modifications of the Carbide, Fe2C-Their Properties and Identification[J]. J Am Chem Soc, 1949, 71(1): 189?195.

[93] [93] LIU Q Y, SHANG C, LIU Z P. In situ active site for Fe-catalyzed fischer-tropsch synthesis: Recent progress and future challenges[J]. J Phys Chem Lett, 2022, 13(15): 3342?3352.

[94] [94] HARUTA M. Size- and support-dependency in the catalysis of gold[J]. Catal Today, 1997, 36(1): 153?166.

[95] [95] HARUTA M, TSUBOTA S, KOBAYASHI T, et al. Low-temperature oxidation of CO over gold supported on TiO2, α-Fe2O3, and Co3O4[J]. J Catal, 1993, 144(1): 175?192.

[96] [96] SEGLER M H S, PREUSS M, WALLER M P. Planning chemical syntheses with deep neural networks and symbolic AI[J]. Nature, 2018, 555(7698): 604?610.

[97] [97] COLEY C W, GREEN W H, JENSEN K F. Machine Learning in Computer-Aided Synthesis Planning[J]. Account Chem Res, 2018, 51(5): 1281?1289.

[98] [98] COLEY C W, JIN W, ROGERS L, et al. A graph-convolutional neural network model for the prediction of chemical reactivity[J]. Chem Sci, 2019, 10(2): 370?377.

[99] [99] SCHWALLER P, LAINO T, GAUDIN T, et al. Molecular transformer: A model for uncertainty-calibrated chemical reaction prediction[J]. ACS Centr Sci, 2019, 5(9): 1572?1583.

[100] [100] FANG Y, LI J, CHEN Y, et al. Experiment and modeling study of glucose pyrolysis: Formation of 3-hydroxy-γ-butyrolactone and 3-(2h)-furanone[J]. Energy Fuels, 2018, 32(9): 9519?9529.

[101] [101] PATWARDHAN P R, SATRIO J A, BROWN R C, et al. Product distribution from fast pyrolysis of glucose-based carbohydrates[J]. J Anal Appl Pyrolysis, 2009, 86(2): 323?330.

[102] [102] MAYES H B, NOLTE M W, BECKHAM G T, et al. The alpha-bet(a) of glucose pyrolysis: Computational and experimental investigations of 5-hydroxymethylfurfural and levoglucosan formation reveal implications for cellulose pyrolysis[J]. ACS Sustain Chem Eng, 2014, 2(6): 1461?1473.

[103] [103] SHI Y F, KANG P L, SHANG C, et al. Methanol synthesis from CO2/CO mixture on Cu-Zn catalysts from microkinetics-guided machine learning pathway search[J]. J Am Chem Soc, 2022, 144(29): 13401?13414.