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Prediction Uncertainty Controlled Computer Model Calibration

stat.ML cs.LG stat.AP Ryan Heejoon Byun, Dayeon Yoon, Won Chang · Oct 22, 2026

Standard computer-model calibration focuses on parameter posteriors, not the predictive accuracy of the calibrated simulator. The authors propose a two-layer framework: a flow-matching model amortizes posterior inference, then conformal risk control tunes parameter sets so the simulator pushforward hits a target miscoverage on synthetic calibration data. This targets the quantity that actually matters downstream—predictive coverage—while exploiting amortization to avoid expensive per-observation MCMC. Experiments on synthetic and real epidemiological data show roughly 5× sharper bands than KOH–MCMC with near-nominal coverage.

Computer-model calibration is usually undertaken in service of prediction, yet neither Bayesian Kennedy-O'Hagan (KOH) calibration nor amortized simulation-based inference is built to control the predictive error of the calibrated simulator. When parameters are weakly identified or the data-model discrepancy is misspecified, the simulator-output bands induced by a nominal posterior level can be far from nominal. We propose a two-layer framework that targets predictive miscoverage directly. First, a conditional flow-matching model learns an amortized posterior for the calibration parameters, trained on simulator outputs perturbed with Gaussian-process discrepancies of varying structure. Second, conformal risk control arranges posterior draws for the target observation into nested candidate sets and selects the smallest one whose fixed-rank pointwise bands attain a prescribed time-averaged miscoverage on a synthetic calibration sample. Under exchangeability of calibration and target observations, the bands control expected miscoverage in finite samples. In a synthetic benchmark, the proposed bands are roughly 20% the width of KOH-MCMC bands with miscoverage near the 10% target. In calibrating an age-structured SEIR model to the 2010 Malawi measles outbreak, they are again sharper and near-nominal, and the weeks they fail to cover coincide with the asymmetric epidemic decline, exposing structural inadequacy of the mechanistic model.

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The Physics Is the Network: Fast, Training-Free Neural Emulation

cs.LG cs.SY eess.SY Luka Todorovic, Kaushal Gianchandani, Sai Ravela · Oct 14, 2026

Neural emulation need not require learning a substitute for known physics. This paper investigates PolyNets that compile continuous-time polynomial dynamics and discrete-time RK4 integration into a single tensor graph, benchmarking the approach on the 1D Korteweg–de Vries equation against classical CPU/GPU solvers and three trained neural models. The central finding is that when governing coefficients are known, the resulting network requires no training yet preserves numerical fidelity while achieving competitive GPU throughput.

Neural emulation need not require learning a substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation of polynomial dynamics with a simple recurrent network for discrete-time integration. When the governing coefficients are known, the resulting tensor graph requires no training and preserves the prescribed numerical scheme while enabling efficient hardware execution and parallel simulation. Using the one-dimensional Korteweg-de Vries equation, we compare PolyNet with CPU and GPU finite-difference Runge-Kutta solvers and three trained neural models: a state-map emulator, a physics-informed predictor, and a learned-tendency integrator. Analytical soliton solutions provide a reference for amplitude and phase errors across grid resolutions, 10^6 dispersively scaled time steps, ensembles of up to 10^4 trajectories, and varying initial amplitudes. PolyNet achieves accuracy comparable to the numerical solvers, including at amplitudes outside the learned models' training conditions. It combines this fidelity with high GPU throughput, approximately constant over the tested resolution range, and favorable ensemble scaling.

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Identification of physiological shock in intensive care units via Bayesian regime switching models

stat.AP stat.ME stat.ML Emmett B. Kendall, Jonathan P. Williams, Curtis B. Storlie et al. · Mar 23, 2026

This paper addresses the critical challenge of detecting occult hemorrhage (internal bleeding) in intensive care units, where delayed diagnosis leads to preventable physiological shock and death. The authors develop a Bayesian regime switching model (RSM) that tracks five latent physiological states—including stable, hemorrhage, and recovery—using longitudinal vital signs (heart rate, MAP, hemoglobin, lactate) and medication history. Applied to 33,924 Mayo Clinic ICU encounters, the model aims to provide interpretable, probabilistic early warnings that outperform standard vital sign monitoring by accounting for autoregressive trends and pre-admission physiological changes.

Detection of occult hemorrhage (i.e., internal bleeding) in patients in intensive care units (ICUs) can pose significant challenges for critical care workers. Because blood loss may not always be clinically apparent, clinicians rely on monitoring vital signs for specific trends indicative of a hemorrhage event. The inherent difficulties of diagnosing such an event can lead to late intervention by clinicians which has catastrophic consequences. Therefore, a methodology for early detection of hemorrhage has wide utility. We develop a Bayesian regime switching model (RSM) that analyzes trends in patients' vitals and labs to provide a probabilistic assessment of the underlying physiological state that a patient is in at any given time. This article is motivated by a comprehensive dataset we curated from Mayo Clinic of 33,924 real ICU patient encounters. Longitudinal response measurements are modeled as a vector autoregressive process conditional on all latent states up to the current time point, and the latent states follow a Markov process. We present a novel Bayesian sampling routine to learn the posterior probability distribution of the latent physiological states, as well as develop an approach to account for pre-ICU-admission physiological changes. A simulation and real case study illustrate the effectiveness of our approach.

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Data Curation for Machine Learning Interatomic Potentials by Determinantal Point Processes

stat.AP cs.LG Joanna Zou, Youssef Marzouk · Mar 23, 2026

Training machine learning interatomic potentials (MLIPs) requires costly quantum mechanical calculations to label atomic configurations. This paper proposes using determinantal point processes (DPPs) to select diverse, informative subsets of configurations, mitigating the computational bottleneck while maintaining model accuracy. Experiments on hafnium oxide systems demonstrate that DPP-based subselection achieves competitive or superior performance compared to existing methods like k-means clustering and MaxVol, offering a probabilistic framework that naturally handles variable training set sizes.

The development of machine learning interatomic potentials faces a critical computational bottleneck with the generation and labeling of useful training datasets. We present a novel application of determinantal point processes (DPPs) to the task of selecting informative subsets of atomic configurations to label with reference energies and forces from costly quantum mechanical methods. Through experiments with hafnium oxide data, we show that DPPs are competitive with existing approaches to constructing compact but diverse training sets by utilizing kernels of molecular descriptors, leading to improved accuracy and robustness in machine learning representations of molecular systems. Our work identifies promising directions to employ DPPs for unsupervised training data curation with heterogeneous or multimodal data, or in online active learning schemes for iterative data augmentation during molecular dynamics simulation.

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Identifiability and amortized inference limitations in Kuramoto models

stat.AP cs.LG Emma Hannula, Jana de Wiljes, Matthew T. Moores et al. · Mar 23, 2026

This paper investigates amortized Bayesian inference (ABI) for estimating coupling parameters in Kuramoto oscillator networks—a nonlinear dynamical system widely used to study synchronization. The authors apply neural posterior estimation via BayesFlow to learn an amortized approximation of the posterior distribution from simulated phase dynamics. While the method succeeds for simple single-parameter networks, the paper's central finding is that it fails for complex multi-node networks due to structural non-identifiability and data inefficiency—making the title's focus on 'limitations' well-earned.

Bayesian inference is a powerful tool for parameter estimation and uncertainty quantification in dynamical systems. However, for nonlinear oscillator networks such as Kuramoto models, widely used to study synchronization phenomena in physics, biology, and engineering, inference is often computationally prohibitive due to high-dimensional state spaces and intractable likelihood functions. We present an amortized Bayesian inference approach that learns a neural approximation of the posterior from simulated phase dynamics, enabling fast, scalable inference without repeated sampling or optimization. Applied to synthetic Kuramoto networks, the method shows promising results in approximating posterior distributions and capturing uncertainty, with computational savings compared to traditional Bayesian techniques. These findings suggest that amortized inference is a practical and flexible framework for uncertainty-aware analysis of oscillator networks.

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