Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This assumption fails for delay equations, distributed-memory systems, and other non-Markovian dynamics: two trajectories may agree at time $t$ and nevertheless have different futures because their histories differ. We introduce the History-Space Fourier Neural Operator (HS-FNO), a neural operator for delay and memory-driven PDEs formulated on the lifted state $u_t(θ,x)=u(t+θ,x)$, $θ\in[-τ,0]$. The key computational step is to decompose one history-state update into a learned predictor for the newly exposed future slice and an exact shift-append transport for the portion of the history window already known from the previous state. This avoids learning deterministic history coordinates, reduces the learned output dimension, and enforces the natural discrete history update. We test HS-FNO on five benchmark families covering delayed reaction--diffusion, spatial epidemiology, nonlocal neural-field dynamics, delayed waves, and distributed-memory closures. Across ten random seeds, HS-FNO attains the lowest aggregate one-step, history-space, and rollout errors among the principal baselines. The largest gain occurs in autoregressive prediction, where aggregate rollout error decreases from $0.241$, $0.188$, and $0.185$ for current-state, lag-stack, and unconstrained history-to-history operators, respectively, to $0.094$. The same model uses fewer parameters than unconstrained history prediction. These results indicate that enforcing the discrete shift structure of history-state evolution is an effective inductive bias for non-Markovian PDE surrogate modeling.

Within a single sniff, the mammalian olfactory system can decode the identity and concentration of odorants wafted on turbulent plumes of air. Yet, it must do so given access only to the noisy, dimensionally-reduced representation of the odor world provided by olfactory receptor neurons. As a result, the olfactory system must solve a compressed sensing problem, relying on the fact that only a handful of the millions of possible odorants are present in a given scene. Inspired by this principle, past works have proposed normative compressed sensing models for olfactory decoding. However, these models have not captured the unique anatomy and physiology of the olfactory bulb, nor have they shown that sensing can be achieved within the 100-millisecond timescale of a single sniff. Here, we propose a rate-based Poisson compressed sensing circuit model for the olfactory bulb.

Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data. Supervised machine learning methods have demonstrated promise in learning efficient surrogate models that can (partially) replace expensive high-fidelity models, making many-query analyses, such as optimization, uncertainty quantification, and inference, tractable. However, when training data must be obtained through the evaluation of an expensive model or experiment, the amount of training data that can be obtained is often limited, which can make learned surrogate models unreliable. However, in many engineering and scientific settings, cheaper \emph{low-fidelity} models may be available, for example arising from simplified physics modeling or coarse grids. These models may be used to generate additional low-fidelity training data. The goal of \emph{multifidelity} machine learning is to use both high- and low-fidelity training data to learn a surrogate model which is cheaper to evaluate than the high-fidelity model, but more accurate than any available low-fidelity model. This work proposes a new multifidelity training approach for Gaussian process regression which uses low-fidelity data to define additional features that augment the input space of the learned model. The approach unites desirable properties from two separate classes of existing multifidelity GPR approaches, cokriging and autoregressive estimators. Numerical experiments on several test problems demonstrate both increased predictive accuracy and reduced computational cost relative to the state of the art.

Anomaly and failure detection methods are crucial in identifying deviations from normal system operational conditions, which allows for actions to be taken in advance, usually preventing more serious damages. Long-lasting deviations indicate failures, while sudden, isolated changes in the data indicate anomalies. However, in many practical applications, changes in the data do not always represent abnormal system states. Such changes may be recognized incorrectly as failures, while being a normal evolution of the system, e.g. referring to characteristics of starting the processing of a new product, i.e. realizing a domain shift. Therefore, distinguishing between failures and such ''healthy'' changes in data distribution is critical to ensure the practical robustness of the system. In this paper, we propose a method that not only detects changes in the data distribution and anomalies but also allows us to distinguish between failures and normal domain shifts inherent to a given process. The proposed method consists of a modified Page-Hinkley changepoint detector for identification of the domain shift and possible failures and supervised domain-adaptation-based algorithms for fast, online anomaly detection. These two are coupled with an explainable artificial intelligence (XAI) component that aims at helping the human operator to finally differentiate between domain shifts and failures. The method is illustrated by an experiment on a data stream from the steel factory.

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and leverage them to solve downstream problems, for example risk-averse formulations. We focus on human choice settings that can be formulated as (integer) linear programs. In such settings, existing inverse optimization and choice modelling methods infer preferences from observed choices but typically produce point estimates or fail to capture contextual shifts, making them unsuitable for risk-averse decision-making. Using a bounded-variance score function gradient estimator, we train a predictive model mapping contextual features to a rich class of parameterizable distributions. This approach yields a maximum likelihood estimate. The model generates scenarios for unseen contexts in the subsequent optimization phase. In a synthetic ridesharing environment, our approach reduces average post-decision surprise by up to 114$\times$ compared to a risk-neutral approach with perfect predictions and up to 25$\times$ compared to leading risk-averse baselines.

The vast amount of data required to model wildfires at a larger scale presents difficulties in the collection and curation of the data.

Let usconsiderasetof C-PROcontextswithlogicrules BOTHor EITHER, andsensoryruleswith values REDor VERTICAL (Figure 1).

This paper will focus on the case of graph classification, but with minor modifications, our framework can beextended toother tasks ofinterest.