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Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying ideas apply more broadly to other observables, like pair-correlation and angular-distribution functions, and other methods, including molecular dynamics. For Pulay-type contributions, we show that a minor modification based on the Metropolis acceptance ratio softens the power-law divergence of the variance to a logarithmic one, thus reducing the tails of the distribution. Proposal averaging can be added to remove this nodal divergence completely or, alternatively, inexpensive regularizations can be applied to suppress remaining outliers at the price of a controlled small bias. For Hellmann\u2013Feynman forces, we derive compact variance-reduced estimators for periodic systems that are straightforward to implement in standard Monte Carlo codes. The approach is illustrated for high-pressure metallic hydrogen with more than a hundred atoms described by neural quantum states, including an application to molecular dynamics driven by the improved forces.<\/jats:p>","DOI":"10.1063\/5.0336683","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:40:09Z","timestamp":1790851209000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Variance reduction for forces and pressure in variational Monte Carlo"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7746-0309","authenticated-orcid":false,"given":"David","family":"Linteau","sequence":"first","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL) 1 , CH-1015 Lausanne,","place":["Switzerland"]},{"name":"Center for Quantum Science and Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL) 2 , CH-1015 Lausanne,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3862-2919","authenticated-orcid":false,"given":"Saverio","family":"Moroni","sequence":"additional","affiliation":[{"name":"CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali and SISSA Scuola Internazionale Superiore di Studi Avanzati 3 , Via Bonomea 265, I-34136 Trieste,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8887-4356","authenticated-orcid":false,"given":"Giuseppe","family":"Carleo","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL) 1 , CH-1015 Lausanne,","place":["Switzerland"]},{"name":"Center for Quantum Science and Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL) 2 , CH-1015 Lausanne,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0803-2732","authenticated-orcid":false,"given":"Markus","family":"Holzmann","sequence":"additional","affiliation":[{"name":"Univ. 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