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1. Ensemble Adaptive Sampling Scheme: Identifying an Optimal Sampling Strategy via Policy Ranking

   https://doi.org/10.1021/acs.jctc.4c01488  

   Nadeem, Hassan; Shukla, Diwakar (April 2025, Journal of Chemical Theory and Computation)

   Efficient sampling in biomolecular simulations is critical for accurately capturing the complex dynamic behaviors of biological systems. Adaptive sampling techniques aim to improve efficiency by focusing computational resources on the most relevant regions of the phase space. In this work, we present a framework for identifying the optimal sampling policy through metric-driven ranking. Our approach systematically evaluates the policy ensemble and ranks the policies based on their ability to explore the conformational space effectively. Through a series of biomolecular simulation case studies, we demonstrate that the choice of a different adaptive sampling policy at each round significantly outperforms single policy sampling, leading to faster convergence and improved sampling performance. This approach takes an ensemble of adaptive sampling policies and identifies the optimal policy for the next round based on current data. Beyond presenting this ensemble view of adaptive sampling, we also propose two sampling algorithms that approximate this ranking framework on the fly. The modularity of this framework allows incorporation of any adaptive sampling policy, making it versatile and suitable as a comprehensive adaptive sampling scheme. 

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2. Adaptive Sampling to Reduce Epistemic Uncertainty Using Prediction Interval-Generation Neural Networks

   https://doi.org/10.1609/aaai.v39i18.34152  

   Morales, Giorgio; Sheppard, John W (April 2025, Proceedings of the AAAI Conference on Artificial Intelligence)

   Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and time-consuming. This paper presents an adaptive sampling approach designed to reduce epistemic uncertainty in predictive models. Our primary contribution is the development of a metric that estimates potential epistemic uncertainty leveraging prediction interval-generation neural networks.This estimation relies on the distance between the predicted upper and lower bounds and the observed data at the tested positions and their neighboring points. Our second contribution is the proposal of a batch sampling strategy based on Gaussian processes (GPs). A GP is used as a surrogate model of the networks trained at each iteration of the adaptive sampling process. Using this GP, we design an acquisition function that selects a combination of sampling locations to maximize the reduction of epistemic uncertainty across the domain.We test our approach on three unidimensional synthetic problems and a multi-dimensional dataset based on an agricultural field for selecting experimental fertilizer rates.The results demonstrate that our method consistently converges faster to minimum epistemic uncertainty levels compared to Normalizing Flows Ensembles, MC-Dropout, and simple GPs. 

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3. Adaptive capacity in ecosystems

   https://doi.org/10.1016/bs.aecr.2019.02.001  

   Angeler, D. G.; Allen, C. R.; Carnaval, A. (March 2020, Advances in ecological research)

   Understanding the adaptive capacity of ecosystems to cope with change is crucial to management. However, unclear and often confusing definitions of adaptive capacity make application of this concept difficult. In this paper, we revisit definitions of adaptive capacity and operationalize the concept. We define adaptive capacity as the latent potential of an ecosystem to alter resilience in response to change. We present testable hypotheses to evaluate complementary attributes of adaptive capacity that may help further clarify the components and relevance of the concept. Adaptive sampling, inference and modeling can reduce key uncertainties incrementally over time and increase learning about adaptive capacity. Such improvements are needed because uncertainty about global change and its effect on the capacity of ecosystems to adapt to social and ecological change is high. 

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4. Adaptive Bayesian inference of Markov transition rates

   https://doi.org/10.1098/rspa.2022.0453  

   Barendregt, Nicholas W.; Webb, Emily G.; Kilpatrick, Zachary P. (February 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation and can be simply extended beyond two-state models to birth–death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations. 

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5. BourGAN: Generative Networks with Metric Embeddings

   Xiao, Chang; Zhong, Peilin; Zheng, Changxi (December 2018, 32nd Conference on Neural Information Processing Systems)

   This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the L2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features. 

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