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Research by Orestis Oikonomou: neuro-symbolic methods for differential equations, geospatial AI, and verification for scientific discovery.

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3 entries

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Paper2026

Neuro-Symbolic AI for Analytical Solutions of Differential Equations

ICML · Published

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

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

Paper details arXiv ↗PDF ↗Code ↗
Paper2026

The Verifier Is Part of the Simulator: Evidence-View Gaming in Agentic Equation Discovery

NeurIPS Workshop: Sim2Science · Under review

Evidence-view gaming: the same fixed verifier rejects a true candidate library with seven samples and five test functions, but recovers its terms with 25 samples and two test functions. A fixed agreement rule checks four views per sample count and can abstain; agreement is not a certificate of truth.
Figure 1 · Sim2Science: evidence-view gaming and fixed agreement across verifier outputs.Original author manuscript figure, cropped and converted to lossless WebP; diagram unchanged. Tabler icons (MIT); license in Credits.

Figure detail

Open original ↗
Evidence-view gaming: the same fixed verifier rejects a true candidate library with seven samples and five test functions, but recovers its terms with 25 samples and two test functions. A fixed agreement rule checks four views per sample count and can abstain; agreement is not a certificate of truth.

Figure 1 · Sim2Science: evidence-view gaming and fixed agreement across verifier outputs.

Original author manuscript figure, cropped and converted to lossless WebP; diagram unchanged. Tabler icons (MIT); license in Credits.

  • Agentic scientific discovery
  • Reward hacking
  • Verifier robustness
  • Weak-form equation discovery

Sim2Science studies evidence-view gaming in agentic equation discovery: an agent can change a fixed verifier's verdict by choosing the numerical summary it admits as evidence. Fixed agreement across several views can reduce errors or abstain, but agreement alone does not certify truth.

Paper details
Paper2026

ZeroFlood: Flood Hazard Mapping from Single-Modality SAR Using Geo-Foundation Models

EUSAR (oral) · Published

ZeroFlood workflow: geophysical data and flood simulations train a geospatial foundation model, deployed with SAR imagery in data-scarce regions.
Figure 1 · ZeroFlood framework. Kim & Oikonomou.Source paper ↗CC BY 4.0Page cropped; converted to WebP. Diagram unchanged.

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ZeroFlood workflow: geophysical data and flood simulations train a geospatial foundation model, deployed with SAR imagery in data-scarce regions.

Figure 1 · ZeroFlood framework. Kim & Oikonomou.

Page cropped; converted to WebP. Diagram unchanged.

Source paper ↗CC BY 4.0
  • Geospatial foundation models
  • Remote sensing
  • SAR
  • Flood hazard mapping

ZeroFlood uses geospatial foundation models to map flood hazards from SAR imagery. It evaluates transfer from simulated European flood data to regions with limited observations.

Paper details arXiv ↗PDF ↗Code ↗