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Knowledge-based Deep Learning for Modeling Chaotic Systems

2022, Elabid, Zakaria, Chakraborty, Tanujit, Hadid, Abdenour

Deep Learning has received increased attention due to its unbeatable success in many fields, such as computer vision, natural language processing, recommendation systems, and most recently in simulating multiphysics problems and predicting nonlinear dynamical systems. However, modeling and forecasting the dynamics of chaotic systems remains an open research problem since training deep learning models requires big data, which is not always available in many cases. Such deep learners can be trained from additional information obtained from simulated results and by enforcing the physical laws of the chaotic systems. This paper considers extreme events and their dynamics and proposes elegant models based on deep neural networks, called knowledge-based deep learning (KDL). Our proposed KDL can learn the complex patterns governing chaotic systems by jointly training on real and simulated data directly from the dynamics and their differential equations. This knowledge is transferred to model and forecast real-world chaotic events exhibiting extreme behavior. We validate the efficiency of our model by assessing it on three real-world benchmark datasets: El Niño sea surface temperature, San Juan Dengue viral infection, and Bjørnøya daily precipitation, all governed by extreme events' dynamics. Using prior knowledge of extreme events and physics-based loss functions to lead the neural network learning, we ensure physically consistent, generalizable, and accurate forecasting, even in a small data regime. Index Terms-Chaotic systems, long short-term memory, deep learning, extreme event modeling.

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When geoscience meets generative AI and large language models: Foundations, trends, and future challenges

2024, Hadid, Abdenour, Chakraborty, Tanujit, Daniel Busby

Generative Artificial Intelligence (GAI) represents an emerging field that promises the creation of synthetic data and outputs in different modalities. GAI has recently shown impressive results across a large spectrum of applications ranging from biology, medicine, education, legislation, computer science, and finance. As one strives for enhanced safety, efficiency, and sustainability, generative AI indeed emerges as a key differentiator and promises a paradigm shift in the field. This article explores the potential applications of generative AI and large language models in geoscience. The recent developments in the field of machine learning and deep learning have enabled the generative model's utility for tackling diverse prediction problems, simulation, and multi‐criteria decision‐making challenges related to geoscience and Earth system dynamics. This survey discusses several GAI models that have been used in geoscience comprising generative adversarial networks (GANs), physics‐informed neural networks (PINNs), and generative pre‐trained transformer (GPT)‐based structures. These tools have helped the geoscience community in several applications, including (but not limited to) data generation/augmentation, super‐resolution, panchromatic sharpening, haze removal, restoration, and land surface changing. Some challenges still remain, such as ensuring physical interpretation, nefarious use cases, and trustworthiness. Beyond that, GAI models show promises to the geoscience community, especially with the support to climate change, urban science, atmospheric science, marine science, and planetary science through their extraordinary ability to data‐driven modelling and uncertainty quantification.

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Probabilistic AutoRegressive Neural Networks for Accurate Long-Range Forecasting

2023, Panja, Madhurima, Chakraborty, Tanujit, Kumar, Uttam, Hadid, Abdenour

Forecasting time series data is a critical area of research with applications spanning from stock prices to early epidemic prediction. While numerous statistical and machine learning methods have been proposed, real-life prediction problems often require hybrid solutions that bridge classical forecasting approaches and modern neural network models. In this study, we introduce a Probabilistic AutoRegressive Neural Network (PARNN), capable of handling complex time series data exhibiting non-stationarity, nonlinearity, non-seasonality, long-range dependence, and chaotic patterns. PARNN is constructed by improving autoregressive neural networks (ARNN) using autoregressive integrated moving average (ARIMA) feedback error. Notably, the PARNN model provides uncertainty quantification through prediction intervals and conformal predictions setting it apart from advanced deep learning tools. Through comprehensive computational experiments, we evaluate the performance of PARNN against standard statistical, machine learning, and deep learning models. Diverse real-world datasets from macroeconomics, tourism, epidemiology, and other domains are employed for short-term, medium-term, and long-term forecasting evaluations. Our results demonstrate the superiority of PARNN across various forecast horizons, surpassing the state-of-the-art forecasters. The proposed PARNN model offers a valuable hybrid solution for accurate long-range forecasting. The ability to quantify uncertainty through prediction intervals further enhances the model’s usefulness in various decision-making processes.

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W-Transformers : A Wavelet-based Transformer Framework for Univariate Time Series Forecasting

2022, Sasal, Lena, Chakraborty, Tanujit, Hadid, Abdenour

Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of transformers, the ability to capture long-range temporal dependencies and interactions is desirable for time series forecasting, leading to its progress in various time series applications. In this paper, we build a transformer model for non-stationary time series. The problem is challenging yet crucially important. We present a novel framework for univariate time series representation learning based on the wavelet-based transformer encoder architecture and call it W-Transformer. The proposed W-Transformers utilize a maximal overlap discrete wavelet transformation (MODWT) to the time series data and build local transformers on the decomposed datasets to vividly capture the nonstationarity and long-range nonlinear dependencies in the time series. Evaluating our framework on several publicly available benchmark time series datasets from various domains and with diverse characteristics, we demonstrate that it performs, on average, significantly better than the baseline forecasters for short-term and long-term forecasting, even for datasets that consist of only a few hundred training samples.