arXiv:2509.03340v4 Announce Type: replace-cross Abstract: Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity, averaging over solutions and failing to represent lower-symmetry outcomes. In this work, we formalize the use of generative AI, specifically flow matching, as a principled way to model the full probability distribution over bifurcation outcomes. Our approach builds on existing techniques by combining flow
The rapid advancement in generative AI, particularly flow matching techniques, is enabling new approaches to complex scientific and engineering problems previously intractable for deterministic models.
This development allows AI to model probabilistic outcomes in systems with symmetry breaking, which is crucial for understanding and predicting behavior in areas like materials science, climate modeling, and engineering design.
Generative AI can now capture the full probability distribution of outcomes in non-linear dynamical systems, moving beyond simple averaging to represent multiple possible stable states.
- · AI researchers and developers
- · Scientists in complex systems
- · Engineering design sectors
- · Materials science
- · Traditional deterministic modeling approaches
- · Those relying solely on averaged system outputs
Improved generative AI models will provide more accurate and nuanced predictions for complex physical and engineering phenomena.
This capability could accelerate discovery in materials science and pharmaceutical development by enabling more effective exploration of design spaces.
The enhanced ability to model branching outcomes might lead to breakthroughs in controlling or exploiting complex system behaviors for novel applications.
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Read at arXiv cs.AI