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Uncertainty-Guided Prediction Horizon of Phase-Resolved Ocean Wave Forecasting Under Data Sparsity: Experimental and Numerical Evaluation

Accurate short-term wave forecasting is critical for the safe and efficient operation of marine structures that rely on real-time, phase-resolved ocean wave information for control and monitoring purposes (e.g., digital twins). These systems often depend on environmental sensors (e.g., waverider buoys, wave-sensing LIDAR). Challenges arise when upstream sensor data are missing, sparse, or phase-shifted due to drift. This study investigates the performance of two machine learning models, time-series dense encoder (TiDE) and long short-term memory (LSTM), for forecasting phase-resolved ocean surface elevations under varying degrees of data degradation. We introduce the τ-trimming algorithm, which adapts the prediction horizon based on uncertainty thresholds derived from historical forecasts. Numerical wave tank (NWT) and wave basin experiments are used to benchmark model performance under short- and long-term data masking, spatially coarse sensor grids, and upstream phase shifts. Results show under a 50% probability of upstream data loss, the τ-trimmed TiDE model achieves a 46% reduction in error at the most upstream target, compared to 22% for LSTM. Furthermore, phase misalignment in upstream data introduces a near-linear increase in forecast error. Under moderate model settings, a ±3 s misalignment increases the mean absolute error by approximately 0.5 m, while the same error is accumulated at ±4 s using the more conservative approach. These findings inform the design of resilient, uncertainty-aware wave forecasting systems suited for realistic offshore sensing environments.

42 ENGINEERING↗

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗

Support for Reactor Operators in Case of Cyber-Security Threats (NEUP Final Report)

Increasing use of digital technology in nuclear power plants (NPPs) poses cyber-security as a crucial threat to public safety and to continuous energy production. Cyber-security risks are comprised of complex known and unknown interactions between various entities, system vulnerabilities, network protocols, human users and malicious attacks. There is little understanding or research geared towards plant operators’ response under cyber-security threats and operational procedures to cope with such threats. This is particularly critical when a cyber-security event masquerades as a safety incident or an evolving accident. Instead of leading operators to the remediation of the accident, the masked cyber event may lead them to circumvent the safety mechanisms of the plant. Given these challenges, the objective of this project is to develop a tool to characterize abnormal NPP events as “cyber” or “safety” incidents, and to further develop this tool as a real-time operator aid to assist in response to the incident. This NEUP Final Report summarizes the research efforts towards the above goals and the results in the following three aspects. First, a methodology for classifying abnormal NPP events as cyber-attacks or safety incidents was developed. This provides the basis for responding to potential cyber-attacks. In this methodology, the causal relationships between various variables (i.e., physical variables, network variables, and control variables) for a nuclear system under consideration are modeled using dynamic Bayesian networks. Based on observations of certain variables (i.e., the evidence), inference is performed to identify the state of hidden variables, which helps indicate the occurrence of cyber-attacks or safety incidents. The proposed methodology was applied to the full scope NPP simulator system at The Ohio State University as a case study. The result shows that the proposed methodology is capable of distinguishing between cyber-attacks and safety incidents. Second, a game-theoretic approach for responding to cyber-attacks on nuclear power plants was developed. This is the second major goal of the project, and the method is used to recommend optimal responses to reactor operators in the case of cyber-attacks. We consider two cases in this research. In the first case, the interaction between the defender (i.e., the reactor operator) and the attacker is modeled as a two-player, nonzero-sum, Markov game with an infinite time horizon. In the second case, we consider a semi-Markov game between the defender and the attacker within a finite time horizon. The model in the second case enables us to consider the time sensitive response of the defender. In each case, the method for deriving the Nash equilibrium is developed. The Nash Equilibrium of the game provides the valid prediction of both players’ actions because no single player can benefit from unilaterally deviating from the equilibrium policy if the other player adheres to his/hers, hence it provides the best response of the defender to cyber-attacks. The proposed method in each case is demonstrated through a simplified benchmark digital feedwater control system. Third, a prototype display is developed to integrate the above information. The prototype display depicts the communication information to the operator and incorporates the cyber-security tool developed by the team into the interface. It consists of the regular display in current control rooms, as well as a panel used to indicate the occurrence of cyber-attacks or safety events and a panel used to guide the operator’s response to detected cyber-attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗