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How to Differentiate Collective Variables in Free Energy Codes: Computer-Algebra Code Generation and Automatic Differentiation

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Toni Giorgino

Computational Physics · Submitted 20 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Users may use the code as a template to streamline the implementation of their own CVs using high-level constructs and automatic gradient computation.

how it is stated · hedged possibility 1.00 read the record →

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arXiv ID1709.06780 (version 2)
Pith IDPHYOYCLX, Pith's permanent record of this paper and its review
CitationToni Giorgino. "How to Differentiate Collective Variables in Free Energy Codes: Computer-Algebra Code Generation and Automatic Differentiation." arXiv:1709.06780 (2017). https://pith.science/paper/PHYOYCLX
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,327 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.33 · mentions code or data availability 0.68.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The proper choice of collective variables (CVs) is central to biased-sampling free energy reconstruction methods in molecular dynamics simulations. The PLUMED 2 library, for instance, provides several sophisticated CV choices, implemented in a C++ framework; however, developing new CVs is still time consuming due to the need to provide code for the analytical derivatives of all functions with respect to atomic coordinates. We present two solutions to this problem, namely (a) symbolic differentiation and code generation, and (b) automatic code differentiation, in both cases leveraging open-source libraries (SymPy and Stan Math respectively). The two approaches are demonstrated and discussed in detail implementing a realistic example CV, the local radius of curvature of a polymer. Users may use the code as a template to streamline the implementation of their own CVs using high-level constructs and automatic gradient computation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The proper choice of collective variables (CVs) is central to biased-sampling free energy reconstruction methods in molecular dynamics simulations. background 1.00 0.06 0.06 asserted 1.00
s1 The PLUMED 2 library, for instance, provides several sophisticated CV choices, implemented in a C++ framework; however, developing new CVs is still time consuming due to the need to provide code for the analytical derivatives of all functions with respect to atomic coordinates. background 0.66 0.08 0.04 asserted 1.00
s2 We present two solutions to this problem, namely (a) symbolic differentiation and code generation, and (b) automatic code differentiation, in both cases leveraging open-source libraries (SymPy and Stan Math respectively). contribution 0.83 0.91 0.31 asserted 1.00
s3 The two approaches are demonstrated and discussed in detail implementing a realistic example CV, the local radius of curvature of a polymer. method 0.50 0.92 0.13 asserted 1.00
s4 Users may use the code as a template to streamline the implementation of their own CVs using high-level constructs and automatic gradient computation. future work 0.49 0.26 0.20 hedged possibility 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.93.

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  • references and citing sentences
  • relations to other papers
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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The proper choice of collective variables (CVs) is central to biased-sampling free energy reconstruction methods in molecular dynamics simulations. The PLUMED 2 library, for instance, provides several sophisticated CV choices, implemented in a C++ framework; however, developing new CVs is still time consuming due to the need to provide code for the analytical derivatives of all functions with respect to atomic coordinates. We present two solutions to this problem, namely (a) symbolic differentiation and code generation, and (b) automatic code differentiation, in both cases leveraging open-source libraries (SymPy and Stan Math respectively). The two approaches are demonstrated and discussed in detail implementing a realistic example CV, the local radius of curvature of a polymer. Users may use the code as a template to streamline the implementation of their own CVs using high-level constructs and automatic gradient computation.

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