This paper introduces an Artificial Intelligence (AI) foundation model for time series in engineering applications, where causal operations are required for real-time monitoring and control. Since engineering time series are governed by physical, rather than linguistic, laws, large-language-model-based AI foundation models may be ineffective or inefficient. Building on the classical innovations representation theory of Wiener, Kallianpur, and Rosenblatt, we propose Time Series GPT (TS-GPT) -- an innovations-representation-based Generative Pre-trained Transformer for engineering monitoring and control. As an example of foundation model adaptation, we consider Probabilistic Generative Forecasting, which produces future time series samples from conditional probability distributions given past realizations. We demonstrate the effectiveness of TS-GPT in forecasting real-time locational marginal prices using historical data from U.S. independent system operators.

This paper presents a generative artificial intelligence approach to probabilistic forecasting of electricity market signals, such as real-time locational marginal prices and area control error signals. Inspired by the Wiener-Kallianpur innovation representation of nonparametric time series, we propose a weak innovation autoencoder architecture and a novel deep learning algorithm that extracts the canonical independent and identically distributed innovation sequence of the time series, from which samples of future time series are generated. The validity of the proposed approach is established by proving that, under ideal training conditions, the generated samples have the same conditional probability distribution as that of the ground truth. Three applications involving highly dynamic and volatile time series in real-time market operations are considered: (i) locational marginal price forecasting for self-scheduled resources such as battery storage participants, (ii) interregional price spread forecasting for virtual bidders in interchange markets, and (iii) area control error forecasting for frequency regulations. Numerical studies based on market data from multiple independent system operators demonstrate the superior performance of the proposed generative forecaster over leading classical and modern machine learning techniques under both probabilistic and point forecasting metrics.

Purpose This article presents a case for a next-generation grid monitoring and control system, leveraging recent advances in generative artificial intelligence (AI), machine learning, and statistical inference. Advancing beyond earlier generations of wide-area monitoring systems built upon supervisory control and data acquisition (SCADA) and synchrophasor technologies, we argue for a monitoring and control framework based on the streaming of continuous point-on-wave (CPOW) measurements with AI-powered data compression and fault detection. Methods and Results: The architecture of the proposed design originates from the Wiener-Kallianpur innovation representation of a random process that transforms causally a stationary random process into an innovation sequence with independent and identically distributed random variables. This work presents a generative AI approach that (i) learns an innovation autoencoder that extracts innovation sequence from CPOW time series, (ii) compresses the CPOW streaming data with innovation autoencoder and subband coding, and (iii) detects unknown faults and novel trends via nonparametric sequential hypothesis testing. Conclusion: This work argues that conventional monitoring using SCADA and phasor measurement unit (PMU) technologies is ill-suited for a future grid with deep penetration of inverter-based renewable generations and distributed energy resources. A monitoring system based on CPOW data streaming and AI data analytics should be the basic building blocks for situational awareness of a highly dynamic future grid.

The main challenge of applying Wiener-Kallianpur innovation Whereas standard probabilistic forecasting aims to estimate representation for inference and decision-making is the conditional probability distribution of the time series at twofold. First, obtaining a causal encoder to extract the a future time, GPF obtains a generative model capable of innovation process requires knowing the marginal and joint producing arbitrarily many Monte Carlo samples of future distributions of the time series, which is rarely possible without time series realizations according to the conditional probability imposing some parametric structure. Furthermore, even when distribution of the time series given past observations. As the probability distribution is known, there is no known computationally a nonparametric probabilistic forecasting technique, GPF is tractable way to construct the causal encoder to essential for decision-making under uncertainty where datadriven obtain an innovation process. Second, the Wiener-Kallianpur risk-sensitive optimization requires conditional samples innovation representation may not exist for a broad class of of future randomness. The Monte Carlo samples generated random processes, including some of the important cases of from GPF can be used to produce any form of point forecast.

Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. Such techniques are critical in risk-based decision-making and planning under uncertainties. Existing approaches are primarily based on parametric or semi-parametric time-series models that are restrictive, difficult to validate, and challenging to adapt to varying conditions. This paper proposes a nonparametric method based on the classic notion of {\em innovations} pioneered by Norbert Wiener and Gopinath Kallianpur that causally transforms a nonparametric random process to an independent and identical uniformly distributed {\em innovations process}. We present a machine-learning architecture and a learning algorithm that circumvent two limitations of the original Wiener-Kallianpur innovations representation: (i) the need for known probability distributions of the time series and (ii) the existence of a causal decoder that reproduces the original time series from the innovations representation. We develop a deep-learning approach and a Monte Carlo sampling technique to obtain a generative model for the predicted conditional probability distribution of the time series based on a weak notion of Wiener-Kallianpur innovations representation. The efficacy of the proposed probabilistic forecasting technique is demonstrated on a variety of electricity price datasets, showing marked improvement over leading benchmarks of probabilistic forecasting techniques.

An innovations sequence of a time series is a sequence of independent and identically distributed random variables with which the original time series has a causal representation. The innovation at a time is statistically independent of the history of the time series. As such, it represents the new information contained at present but not in the past. Because of its simple probability structure, an innovations sequence is the most efficient signature of the original. Unlike the principle or independent component analysis representations, an innovations sequence preserves not only the complete statistical properties but also the temporal order of the original time series. An long-standing open problem is to find a computationally tractable way to extract an innovations sequence of non-Gaussian processes. This paper presents a deep learning approach, referred to as Innovations Autoencoder (IAE), that extracts innovations sequences using a causal convolutional neural network. An application of IAE to the one-class anomalous sequence detection problem with unknown anomaly and anomaly-free models is also presented.