Neural Quantum States for Scientific Computing: Applications to Computational Chemistry and Finance
dc.contributor.author | Zhao, Tianchen | |
dc.date.accessioned | 2022-09-06T16:00:23Z | |
dc.date.available | 2022-09-06T16:00:23Z | |
dc.date.issued | 2022 | |
dc.date.submitted | 2022 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/174223 | |
dc.description.abstract | The variational quantum Monte Carlo (VQMC) method has received significant attention because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems, by representing the exponentially complex quantum states variationally with machine learning models. We develop novel training strategies to improve the scalability of VQMC, and build parallelization frameworks for solving large-scale problems. The application of our method is extended to quantum chemistry and financial derivative pricing. For quantum chemistry, we build a pre-processing pipeline serving as an interface connecting molecular information and VQMC, and achieve remarkable performance in comparison with the classical approximate methods. On the other hand, we present a simple generalization of VQMC applicable to arbitrary linear PDEs, showcasing the technique in the Black-Scholes equation for pricing European contingent claims dependent on many underlying assets. We also introduce meta-learning and multi-fidelity active learning as exotic components to VQMC, which, under some reasonable assumptions on the problem formulation, can further improve the convergence and the sampling efficiency of our method. | |
dc.language.iso | en_US | |
dc.subject | variational quantum Monte Carlo | |
dc.title | Neural Quantum States for Scientific Computing: Applications to Computational Chemistry and Finance | |
dc.type | Thesis | |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Applied and Interdisciplinary Mathematics | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.contributor.committeemember | Veerapaneni, Shravan | |
dc.contributor.committeemember | Gavini, Vikram | |
dc.contributor.committeemember | Cohen, Asaf | |
dc.contributor.committeemember | Stokes, James | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbtoplevel | Science | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/174223/1/ericolon_1.pdf | |
dc.identifier.doi | https://dx.doi.org/10.7302/5954 | |
dc.identifier.orcid | 0000-0003-2911-7205 | |
dc.identifier.name-orcid | Zhao, Tianchen; 0000-0003-2911-7205 | en_US |
dc.working.doi | 10.7302/5954 | en |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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