{"id":35140,"date":"2026-04-13T14:10:33","date_gmt":"2026-04-13T14:10:33","guid":{"rendered":"https:\/\/lamarr-institute.org\/publication\/foundation-inference-models-for-ordinary-differential-equations\/"},"modified":"2026-06-08T13:17:50","modified_gmt":"2026-06-08T13:17:50","slug":"foundation-inference-models-for-ordinary-differential-equations","status":"publish","type":"publication","link":"https:\/\/lamarr-institute.org\/de\/publication\/foundation-inference-models-for-ordinary-differential-equations\/","title":{"rendered":"Foundation Inference Models for Ordinary Differential Equations"},"content":{"rendered":"<p>Ordinary differential equations ({ODEs}) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process ({GP}) regression, and Neural {ODEs} often require complex training pipelines and substantial machine learning expertise, or they depend strongly on system-specific prior knowledge. We propose {FIM}-{ODE}, a pretrained Foundation Inference Model that amortises low-dimensional {ODE} inference by predicting the vector field directly from noisy trajectory data in a single forward pass. We pretrain {FIM}-{ODE} on a prior distribution over {ODEs} with low-degree polynomial vector fields and represent the target field with neural operators. {FIM}-{ODE} achieves strong zero-shot performance, matching and often improving upon {ODEFormer}, a recent pretrained symbolic baseline, across a range of regimes despite using a simpler pretraining prior distribution. Pretraining also provides a strong initialisation for finetuning, enabling fast and stable adaptation that outperforms modern neural and {GP} baselines without requiring machine learning expertise.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ordinary differential equations ({ODEs}) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process ({GP}) regression, and Neural {ODEs} often require complex training pipelines and substantial machine learning expertise, or they depend strongly on system-specific prior knowledge. We propose {FIM}-{ODE}, a pretrained Foundation Inference Model that amortises low-dimensional {ODE} inference by predicting the vector field directly from [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":0,"template":"","meta":{"_acf_changed":false,"footnotes":""},"publication-type":[30],"class_list":["post-35140","publication","type-publication","status-publish","hentry","publication-type-article"],"acf":[],"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/35140","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/types\/publication"}],"author":[{"embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":0,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/35140\/revisions"}],"wp:attachment":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/media?parent=35140"}],"wp:term":[{"taxonomy":"publication-type","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-type?post=35140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}