Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions
An efficient and expressive wave function Ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wave function Ansätze, this construction can result in limited expressiveness when the...
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2024-12-01
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| Series: | APL Machine Learning |
| Online Access: | http://dx.doi.org/10.1063/5.0229620 |
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| author | Luca Thiede Chong Sun Alán Aspuru-Guzik |
| author_facet | Luca Thiede Chong Sun Alán Aspuru-Guzik |
| author_sort | Luca Thiede |
| collection | DOAJ |
| description | An efficient and expressive wave function Ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wave function Ansätze, this construction can result in limited expressiveness when the targeted wave function is highly complex. In this work, we introduce Waveflow, an innovative framework for learning many-body fermionic wave functions using boundary-conditioned normalizing flows. Instead of relying on Slater determinants, Waveflow imposes antisymmetry by defining the fundamental domain of the wave function and applying necessary boundary conditions. A key challenge in using normalizing flows for this purpose is addressing the topological mismatch between the prior and target distributions. We propose using O-spline priors and I-spline bijections to handle this mismatch, which allows for flexibility in the node number of the distribution while automatically maintaining its square-normalization property. We apply Waveflow to a one-dimensional many-electron system, where we variationally minimize the system’s energy using variational quantum Monte Carlo (VQMC). Our experiments demonstrate that Waveflow can effectively resolve topological mismatches and faithfully learn the ground-state wave function. |
| format | Article |
| id | doaj-art-4e555d7a719045a99096a5d1d226e745 |
| institution | DOAJ |
| issn | 2770-9019 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Machine Learning |
| spelling | doaj-art-4e555d7a719045a99096a5d1d226e7452025-08-20T02:56:11ZengAIP Publishing LLCAPL Machine Learning2770-90192024-12-0124046106046106-1210.1063/5.0229620Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functionsLuca Thiede0Chong Sun1Alán Aspuru-Guzik2Department of Computer Science, University of Toronto, Toronto, Ontario M5S 2E4, CanadaDepartment of Computer Science, University of Toronto, Toronto, Ontario M5S 2E4, CanadaDepartment of Computer Science, University of Toronto, Toronto, Ontario M5S 2E4, CanadaAn efficient and expressive wave function Ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wave function Ansätze, this construction can result in limited expressiveness when the targeted wave function is highly complex. In this work, we introduce Waveflow, an innovative framework for learning many-body fermionic wave functions using boundary-conditioned normalizing flows. Instead of relying on Slater determinants, Waveflow imposes antisymmetry by defining the fundamental domain of the wave function and applying necessary boundary conditions. A key challenge in using normalizing flows for this purpose is addressing the topological mismatch between the prior and target distributions. We propose using O-spline priors and I-spline bijections to handle this mismatch, which allows for flexibility in the node number of the distribution while automatically maintaining its square-normalization property. We apply Waveflow to a one-dimensional many-electron system, where we variationally minimize the system’s energy using variational quantum Monte Carlo (VQMC). Our experiments demonstrate that Waveflow can effectively resolve topological mismatches and faithfully learn the ground-state wave function.http://dx.doi.org/10.1063/5.0229620 |
| spellingShingle | Luca Thiede Chong Sun Alán Aspuru-Guzik Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions APL Machine Learning |
| title | Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions |
| title_full | Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions |
| title_fullStr | Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions |
| title_full_unstemmed | Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions |
| title_short | Waveflow: Boundary-conditioned normalizing flows applied to fermionic wave functions |
| title_sort | waveflow boundary conditioned normalizing flows applied to fermionic wave functions |
| url | http://dx.doi.org/10.1063/5.0229620 |
| work_keys_str_mv | AT lucathiede waveflowboundaryconditionednormalizingflowsappliedtofermionicwavefunctions AT chongsun waveflowboundaryconditionednormalizingflowsappliedtofermionicwavefunctions AT alanaspuruguzik waveflowboundaryconditionednormalizingflowsappliedtofermionicwavefunctions |