Reducing Training Data Needs with Minimal Multilevel Machine Learning (M3L)
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| Format: | Preprint |
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2023
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| author | Heinen, Stefan Khan, Danish von Rudorff, Guido Falk Karandashev, Konstantin Arrieta, Daniel Jose Arismendi Price, Alastair J. A. Nandi, Surajit Bhowmik, Arghya Hermansson, Kersti von Lilienfeld, O. Anatole |
| author_facet | Heinen, Stefan Khan, Danish von Rudorff, Guido Falk Karandashev, Konstantin Arrieta, Daniel Jose Arismendi Price, Alastair J. A. Nandi, Surajit Bhowmik, Arghya Hermansson, Kersti von Lilienfeld, O. Anatole |
| contents | For many machine learning applications in science, data acquisition, not training, is the bottleneck even when avoiding experiments and relying on computation and simulation. Correspondingly, and in order to reduce cost and carbon footprint, training data efficiency is key. We introduce minimal multilevel machine learning (M3L) which optimizes training data set sizes using a loss function at multiple levels of reference data in order to minimize a combination of prediction error with overall training data acquisition costs (as measured by computational wall-times). Numerical evidence has been obtained for calculated atomization energies and electron affinities of thousands of organic molecules at various levels of theory including HF, MP2, DLPNO-CCSD(T), DFHFCABS, PNOMP2F12, and PNOCCSD(T)F12, and treating tens with basis sets TZ, cc-pVTZ, and AVTZ-F12. Our M3L benchmarks for reaching chemical accuracy in distinct chemical compound sub-spaces indicate substantial computational cost reductions by factors of $\sim$ 1.01, 1.1, 3.8, 13.8 and 25.8 when compared to heuristic sub-optimal multilevel machine learning (M2L) for the data sets QM7b, QM9$^\mathrm{LCCSD(T)}$, EGP, QM9$^\mathrm{CCSD(T)}_\mathrm{AE}$, and QM9$^\mathrm{CCSD(T)}_\mathrm{EA}$, respectively. Furthermore, we use M2L to investigate the performance for 76 density functionals when used within multilevel learning and building on the following levels drawn from the hierarchy of Jacobs Ladder:~LDA, GGA, mGGA, and hybrid functionals. Within M2L and the molecules considered, mGGAs do not provide any noticeable advantage over GGAs. Among the functionals considered and in combination with LDA, the three on average top performing GGA and Hybrid levels for atomization energies on QM9 using M3L correspond respectively to PW91, KT2, B97D, and $τ$-HCTH, B3LYP$\ast$(VWN5), TPSSH. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11196 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reducing Training Data Needs with Minimal Multilevel Machine Learning (M3L) Heinen, Stefan Khan, Danish von Rudorff, Guido Falk Karandashev, Konstantin Arrieta, Daniel Jose Arismendi Price, Alastair J. A. Nandi, Surajit Bhowmik, Arghya Hermansson, Kersti von Lilienfeld, O. Anatole Chemical Physics For many machine learning applications in science, data acquisition, not training, is the bottleneck even when avoiding experiments and relying on computation and simulation. Correspondingly, and in order to reduce cost and carbon footprint, training data efficiency is key. We introduce minimal multilevel machine learning (M3L) which optimizes training data set sizes using a loss function at multiple levels of reference data in order to minimize a combination of prediction error with overall training data acquisition costs (as measured by computational wall-times). Numerical evidence has been obtained for calculated atomization energies and electron affinities of thousands of organic molecules at various levels of theory including HF, MP2, DLPNO-CCSD(T), DFHFCABS, PNOMP2F12, and PNOCCSD(T)F12, and treating tens with basis sets TZ, cc-pVTZ, and AVTZ-F12. Our M3L benchmarks for reaching chemical accuracy in distinct chemical compound sub-spaces indicate substantial computational cost reductions by factors of $\sim$ 1.01, 1.1, 3.8, 13.8 and 25.8 when compared to heuristic sub-optimal multilevel machine learning (M2L) for the data sets QM7b, QM9$^\mathrm{LCCSD(T)}$, EGP, QM9$^\mathrm{CCSD(T)}_\mathrm{AE}$, and QM9$^\mathrm{CCSD(T)}_\mathrm{EA}$, respectively. Furthermore, we use M2L to investigate the performance for 76 density functionals when used within multilevel learning and building on the following levels drawn from the hierarchy of Jacobs Ladder:~LDA, GGA, mGGA, and hybrid functionals. Within M2L and the molecules considered, mGGAs do not provide any noticeable advantage over GGAs. Among the functionals considered and in combination with LDA, the three on average top performing GGA and Hybrid levels for atomization energies on QM9 using M3L correspond respectively to PW91, KT2, B97D, and $τ$-HCTH, B3LYP$\ast$(VWN5), TPSSH. |
| title | Reducing Training Data Needs with Minimal Multilevel Machine Learning (M3L) |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2308.11196 |