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In-context learning to predict critical transitions in dynamical systems

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: Switching and law-discovery dynamics · 0 citations (OpenAlex)

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Introduces TipPFN, a transformer prior-data fitted network trained on a synthetic tipping-system generator (TipBox) to predict relative distance to criticality from short noisy time series via in-context and zero-shot inference.

Problem

Early warning of critical transitions (tipping points) from scarce, short, noisy, partially observed time series, where classical indicators (AR1, variance) and specialized deep classifiers fail to generalize across tipping mechanisms and systems.

Approach

Train a PFN on a synthetic prior that embeds canonical b-tipping normal forms (fold, Hopf, transcritical) into randomized high-dimensional nonlinear SDEs, with relative distance to criticality (RDTC) as a continuous target and causal attention over query plus context episodes, so that inference is amortized and context can be used at test time.

Key results

• Fixed-config TipPFN with 2 context episodes reaches average pre-tip AUROC 0.859 across all datasets versus 0.572 for the best EWS (variance) and 0.613 for Bury.
• On the R-AMOC semi-real system, TipPFN (2c) reaches AUROC 0.913 versus 0.270 for variance EWS.
• On canonical B-Fold, TipPFN (2c) reaches AUROC 0.955 versus 0.633 for variance EWS.

Surprising findings

• Bury's P_tip baseline beats TipPFN on B-AMOC (.948 vs .940 for 2c) and the variance EWS beats TipPFN on TAC.
• TipPFN with 0 context episodes is best on R-Compost, outperforming context-based variants.

Limitations

• Real-world evaluation relies on surrogate RDTC targets derived from empirical transition markers rather than true labels.
• Performance is not uniform: TipPFN with 1 context is weaker on SWEC-iEEG and R-Compost is best with zero context but lower with more context.
• Relies on causal, fixed-after-pretraining prior; online adaptation is left to future work.

Experimental setup

Datasets: TipBox synthetic data SWEC-iEEG TAC DaphniaExt AMOC power-grid blackout microcosm cyanobacteria

Benchmarks: TipBox canonical (B-Fold, B-Hopf, B-Transcritical) semi-real systems (B-Harvest, B-RM TC, B-RM Hopf, B-SEIRx, B-AMOC, R-Bautin, R-SN, R-Compost, R-AMOC) SWEC-iEEG TAC DaphniaExt

Metrics: AUROC lead-time analysis

Baselines: AR1 variance skewness Kendall-tau EWS Bury Huang Zhuge TabPFN 2.6

Builds on: TabPFN prior-data fitted networks critical slowing down early warning signals AUTO-07P

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