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ICMLPublished2026

Neuro-Symbolic AI for Analytical Solutions of Differential Equations

Authors: O. Oikonomou, L. Lingsch, D. Grund, S. Mishra, G. Kissas

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SIGS method: a formal grammar generates atoms assembled by an Ansatz; a topology-regularised grammar variational autoencoder represents expressions for clustering-based structure search and coefficient refinement, guided by equation and initial or boundary residuals.
SIGS method · grammar, latent representation, structure search and coefficient refinement.Source paper ↗AI-assisted illustration authored for this website. See Oikonomou et al. for the original paper framework.

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SIGS method: a formal grammar generates atoms assembled by an Ansatz; a topology-regularised grammar variational autoencoder represents expressions for clustering-based structure search and coefficient refinement, guided by equation and initial or boundary residuals.

SIGS method · grammar, latent representation, structure search and coefficient refinement.

AI-assisted illustration authored for this website. See Oikonomou et al. for the original paper framework.

Source paper ↗

Research summary

SIGS searches grammar-valid symbolic expressions and refines their coefficients against differential-equation residuals and boundary or initial conditions, without solution data.

Research topics

  • Neuro-symbolic AI
  • Differential equations
  • Symbolic discovery
  • Formal grammars
  • Scientific machine learning

More research

Research portfolio of Orestis Oikonomou.