Time Series Foundation Models and Deep Learning Architectures for Earthquake Temporal and Spatial Nowcasting

Alireza Jafari; Geoffrey Fox; John B. Rundle; Andrea Donnellan; Lisa Grant Ludwig

Home/Archive/arXiv

arXiv · 2408.11990

Time Series Foundation Models and Deep Learning Architectures for Earthquake Temporal and Spatial Nowcasting

Alireza Jafari·Geoffrey Fox·John B. Rundle·Andrea Donnellan·Lisa Grant Ludwig

View original source ↗Read source document ↗Export metadata ↓

Abstract

Advancing the capabilities of earthquake nowcasting, the real-time forecasting of seismic activities remains a crucial and enduring objective aimed at reducing casualties. This multifaceted challenge has recently gained attention within the deep learning domain, facilitated by the availability of extensive, long-term earthquake datasets. Despite significant advancements, existing literature on earthquake nowcasting lacks comprehensive evaluations of pre-trained foundation models and modern deep learning architectures. These architectures, such as transformers or graph neural networks, uniquely focus on different aspects of data, including spatial relationships, temporal patterns, and multi-scale dependencies. This paper addresses the mentioned gap by analyzing different architectures and introducing two innovation approaches called MultiFoundationQuake and GNNCoder. We formulate earthquake nowcasting as a time series forecasting problem for the next 14 days within 0.1-degree spatial bins in Southern California, spanning from 1986 to 2024. Earthquake time series is forecasted as a function of logarithm energy released by quakes. Our comprehensive evaluation employs several key performance metrics, notably Nash-Sutcliffe Efficiency and Mean Squared Error, over time in each spatial region. The results demonstrate that our introduced models outperform other custom architectures by effectively capturing temporal-spatial relationships inherent in seismic data. The performance of existing foundation models varies significantly based on the pre-training datasets, emphasizing the need for careful dataset selection. However, we introduce a new general approach termed MultiFoundationPattern that combines a bespoke pattern with foundation model results handled as auxiliary streams. In the earthquake case, the resultant MultiFoundationQuake model achieves the best overall performance.

Explore related subjects

cs.LG physics.geo-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Alireza Jafari, Geoffrey Fox, John B. Rundle, Andrea Donnellan, Lisa Grant Ludwig. 2024-08-21. Time Series Foundation Models and Deep Learning Architectures for Earthquake Temporal and Spatial Nowcasting. https://arxiv.org/abs/2408.11990

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG↗

arXiv2026

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG↗

arXiv2026

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

cs.LG↗