Carson Dudley

Carson Dudley, Yutong Bi, Xiaofeng Liu et al.

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new dynamics on the fly. Transformer-based foundation models increasingly rely on in-context learning for time series forecasting, tabular prediction, and continuous control. As these models are deployed in non-stationary environments, understanding their ability to detect and adapt to regime shifts is important. We formalize this as an in-context change-point detection problem and formally establish the existence of transformer models that solve this problem. Our construction demonstrates that model complexity, in layers and parameters, depends on the level of information available about the change-point location, from no knowledge to knowing exact timing. We validate our results with experiments on synthetic linear regression and linear dynamical systems, where trained transformers match the performance of optimal baselines across information levels. We also show that encoding and incorporating changepoint knowledge indeed improves the real-world performance of a pretrained foundation models on infectious disease forecasting and on financial volatility forecasting around Federal Open Market Committee (FOMC) announcements without retraining, demonstrating practical applicability to real-world regime changes.

Carson Dudley, Samet Oymak

Chain-of-thought and more broadly test-time compute are known to augment the expressive capabilities of language models and have led to major innovations in reasoning. Motivated by this success, this paper explores latent chain-of-thought as well as the impact of depth and looping for time-series and tabular data. We propose a recurrent scheme in which a structured-data transformer, after an initial forward pass, compresses its query-position hidden states into feedback tokens that are appended to the input and processed again, allowing multiple rounds of latent computation before prediction. We compare CoT models against a same-depth no-CoT baseline, a deeper baseline matched to the CoT model in effective depth, and a looped transformer with weight-tied recurrence but no additional chain-of-thought tokens. Across 36 datasets in time-series forecasting and tabular prediction, latent chain-of-thought improves over the baseline on 8/9 time-series datasets (+10.99\% average gain) and 22/27 tabular datasets (+5.31\% average gain). Across both settings, the CoT models perform the best on average. These results demonstrate that chain-of-thought is a useful axis for scaling test-time compute for structured data.

Carson Dudley, Reiden Magdaleno, Christopher Harding et al.

Scientific modeling faces a tradeoff: mechanistic models provide scientific grounding but struggle with real-world complexity, while machine learning models achieve strong predictive performance but require large labeled datasets and are not interpretable. We introduce Simulation-Grounded Neural Networks (SGNNs), which use mechanistic simulations as training data for neural networks. SGNNs are pretrained on synthetic corpora spanning diverse model structures, parameter regimes, stochasticity, and observational artifacts. Simulation-grounded learning has been applied in multiple domains (e.g., surrogate models in physics, forecasting in epidemiology). We provide a unified framework for simulation-grounded learning and evaluated SGNNs across scientific disciplines and modeling tasks. We found that SGNNs were successful across domains: for prediction tasks, they nearly tripled COVID-19 forecasting skill versus CDC baselines, reduced chemical yield prediction error by one-third, and maintained accuracy in ecological forecasting where task-specific models failed. For inference tasks, SGNNs also accurately classified the source of information spread in simulated social networks and enabled supervised learning for unobservable targets, such as estimating COVID-19 transmissibility more accurately than traditional methods even in early outbreaks. Finally, SGNNs enable back-to-simulation attribution, a form of mechanistic interpretability. Back-to-simulation attribution matches real-world observations to the training simulations the model considers most similar, identifying which mechanistic processes the model believes best explain the observed data. By providing a unified framework for simulation-grounded learning, we establish when and how mechanistic simulations can serve as effective training data for robust, interpretable scientific inference.

Carson Dudley, Reiden Magdaleno, Christopher Harding et al.

Infectious disease forecasting in novel outbreaks or low-resource settings is hampered by the need for disease-specific data, bespoke training, and expert tuning. We introduce Mantis, a foundation model trained entirely on mechanistic simulations, which enables out-of-the-box forecasting across diseases, regions, and outcomes, even in settings with limited historical data. We evaluated Mantis against 48 forecasting models across six diseases with diverse transmission modes, assessing both point forecast accuracy (mean absolute error) and probabilistic performance (weighted interval score and coverage). Despite using no real-world data during training, Mantis achieved lower mean absolute error than all models in the CDC's COVID-19 Forecast Hub when backtested on early pandemic forecasts. Across all other diseases tested, including respiratory, vector-borne, and waterborne pathogens, Mantis consistently ranked in the top two models across all evaluation metrics. Notably, Mantis generalized to diseases with transmission mechanisms not represented in its training data, demonstrating that it captures fundamental contagion dynamics rather than memorizing disease-specific patterns. These capabilities position Mantis as a practical foundation for disease forecasting: general-purpose, accurate, and deployable where traditional models fail.

Carson Dudley, Marisa Eisenberg

Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved, but lack a formal underpinning. We place SGNNs in a unified statistical framework. Under standard loss functions, they can be interpreted as amortized Bayesian predictors trained under a simulator-induced prior. Empirical risk minimization then yields convergence to the Bayes-optimal predictor under the synthetic distribution. We employ classical results on distribution shift to characterize how performance degrades when the simulator diverges from reality. Beyond these consequences, we develop SGNN-specific results: (i) conditions under which unobserved scientific parameters are learnable via simulation, and (ii) a back-to-simulation attribution method that provides mechanistic explanations of predictions by linking them to the simulations the model deems similar, with guarantees of posterior consistency. We provide numerical experiments to validate theoretical predictions. SGNNs recover latent parameters, remain robust under mismatch, and outperform classical tools: in a model selection task, SGNNs achieve half the error of AIC in distinguishing mechanistic dynamics. These results establish SGNNs as a principled and practical framework for scientific prediction in data-limited regimes.