Adaptive tensor train metadynamics for high-dimensional free energy exploration
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916057262850048 |
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| author | Strand, Nils E. Yang, Siyao Khoo, Yuehaw Dinner, Aaron R. |
| author_facet | Strand, Nils E. Yang, Siyao Khoo, Yuehaw Dinner, Aaron R. |
| contents | A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in the case of the widely-used metadynamics method, the computational cost of evaluating and storing the bias potential grows exponentially with the number of dimensions. Here, we introduce TT-Metadynamics, in which the accumulated sum of Gaussian functions in the original metadynamics method is periodically compressed into a low-rank tensor train (TT) representation. The TT enables efficient memory use and prevents the computational cost of evaluating the bias potential from increasing with simulation time. We present a "sketching" algorithm that allows us to construct the TT with linear scaling in the number of CVs. Applied to benchmark systems with up to 14 CVs, the accuracy of TT-Metadynamics matches or exceeds that of standard metadynamics in long simulations, particularly in systems with high barriers. These results establish TT-Metadynamics as a scalable and effective method for computing free energies that are functions of several CVs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive tensor train metadynamics for high-dimensional free energy exploration Strand, Nils E. Yang, Siyao Khoo, Yuehaw Dinner, Aaron R. Chemical Physics Statistical Mechanics Computational Physics A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in the case of the widely-used metadynamics method, the computational cost of evaluating and storing the bias potential grows exponentially with the number of dimensions. Here, we introduce TT-Metadynamics, in which the accumulated sum of Gaussian functions in the original metadynamics method is periodically compressed into a low-rank tensor train (TT) representation. The TT enables efficient memory use and prevents the computational cost of evaluating the bias potential from increasing with simulation time. We present a "sketching" algorithm that allows us to construct the TT with linear scaling in the number of CVs. Applied to benchmark systems with up to 14 CVs, the accuracy of TT-Metadynamics matches or exceeds that of standard metadynamics in long simulations, particularly in systems with high barriers. These results establish TT-Metadynamics as a scalable and effective method for computing free energies that are functions of several CVs. |
| title | Adaptive tensor train metadynamics for high-dimensional free energy exploration |
| topic | Chemical Physics Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2603.13549 |