A library of reusable structures, not just paper summaries
ISOM organizes research by mathematical motifs such as symmetry, transport, criticality, topology, and inverse problems so readers can see which structures may transfer into AI.
Published Structural Motifs
Each motif page explains the physics side, AI side, failure modes, and open questions for a reusable structure.
Symmetry / Equivariance
Track when a model should preserve structure under transformations instead of relearning the same relation from scratch.
Conservation Laws / Constraint-Preserving Learning
Ask whether a model should carry forward a quantity, feasibility condition, or budget exactly instead of learning to approximate it softly.
Diffusion / Transport
Model representation change as movement through a medium, not just interpolation between endpoints.
Variational Principles / Energy Minimization
Recast learning or control as selecting the lowest-cost admissible configuration under a structured energy functional.
Phase Transition / Criticality
Look for threshold behavior where small local changes trigger regime shifts, then ask whether the AI system should detect or exploit that boundary.
Multiscale / Renormalization
Treat the problem as one of carrying the right information across scales instead of solving every level independently.
Topology / Graph Constraints
Preserve connectivity and admissible structure when geometry alone is not enough to define a valid solution.
Inverse Problems / Uncertainty-Aware Inference
Separate what the observation process makes identifiable from what the model is merely guessing.