Universal approximation of symmetric and anti-symmetric functions

Journal Article · 26 May 2022 · Communications in Mathematical Sciences

DOI: https://doi.org/10.4310/cms.2022.v20.n5.a8 · OSTI ID:1898106

Han, Jiequn ^[1]; Li, Yingzhou ^[2]; Lin, Lin ^[3]; Lu, Jianfeng ^[4]; Zhang, Jiefu ^[5]; Zhang, Linfeng ^[6]

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1. Princeton Univ., NJ (United States); Flatiron Institute, New York, NY (United States)
2. Fudan Univ., Shanghai (China)
3. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
4. Duke Univ., Durham, NC (United States)
5. Univ. of California, Berkeley, CA (United States)
6. Princeton Univ., NJ (United States)

In this work, we consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ϵ. While the approximation still suffers from the curse of dimensionality, to the best of our knowledge, these are the first results in the literature with explicit error bounds for functions with symmetry or anti-symmetry constraints

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
• Grant/Contract Number: AC02-05CH11231; SC0017867; DMS-1454939; ACI-1450280
• OSTI ID: 1898106
• Journal Information: Communications in Mathematical Sciences, Vol. 20, Issue 5; ISSN 1539-6746
• Publisher: International PressCopyright Statement
• Country of Publication: United States
• Language: English