{"doi":"10.1103/physreve.106.065303","title":"Machine-learning-based data-driven discovery of nonlinear phase-field dynamics","abstract":"One of the main questions regarding complex systems at large scales concerns the effective interactions and driving forces that emerge from the detailed microscopic properties. Coarse-grained models aim to describe complex systems in terms of coarse-scale equations with a reduced number of degrees of freedom. Recent developments in machine-learning algorithms have significantly empowered the discovery process of governing equations directly from data. However, it remains difficult to discover partial differential equations (PDEs) with high-order derivatives. In this paper, we present data-driven architectures based on a multilayer perceptron, a convolutional neural network (CNN), and a combination of a CNN and long short-term memory structures for discovering the nonlinear equations of motion for phase-field models with nonconserved and conserved order parameters. The well-known Allen-Cahn, Cahn-Hilliard, and phase-field crystal models were used as test cases. Two conceptually different types of implementations were used: (a) guided by physical intuition (such as the local dependence of the derivatives) and (b) in the absence of any physical assumptions (black-box model). We show that not only can we effectively learn the time derivatives of the field in both scenarios, but we can also use the data-driven PDEs to propagate the field in time and achieve results in good agreement with the original PDEs.","journal":"Physical review. E","year":2022,"id":262755,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":14,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9548,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2022-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":918682,"name":"Steven A. Silber","orcid":"0000-0002-4983-6963","position":1,"is_corresponding":false},{"id":556175,"name":"Mahdi Kooshkbaghi","orcid":"0000-0002-6344-7382","position":2,"is_corresponding":false},{"id":747201,"name":"Jonathan F. Lovell","orcid":"0000-0002-8626-3033","position":3,"is_corresponding":false},{"id":918681,"name":"Elham Kiyani","orcid":"0000-0002-0970-4034","position":0,"is_corresponding":true}],"reference_count":60,"raw_metadata":null,"created_at":"2026-07-19T00:26:25.074177Z","pmid":"36671129","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}