High Resolution Generative Waveform Modeling Using Denoising Diffusion

The North Sea plays a strategic role in the transition towards the green economy, as it hosts many offshore wind farms and carbon capture and storage (CCS) sites. The North Sea is characterized by moderate seismicity. For example, the 2023 Mw 5.1 North Sea earthquake was the largest earthquake in the region in 33 years, and led to a temporary shutdown of production of Equinor’s oil platform Snorre B.The last comprehensive seismic hazard assessment of the North Sea was performed about twenty years ago (Bungum et al. 2000). Since then, there have been many new ground motions recorded from both onshore and offshore seismic stations in the North Sea region, as well as major advancements in probabilistic seismic hazard assessment (PSHA) methodology. As a result, this study aims to develop the first region-specific ground-motion model for the North Sea, which will be used in an updated PSHA to ensure the safe design of new offshore wind farms and CCS sites.This research forms a part of the SHARP-Storage project, an interdisciplinary Accelerating CCS Technologies project developing improved methods for quantitative assessment of subsurface CO2 storage containment risks. The SHARP project compiled a dataset of North Sea ground-motion records, which comprises data on natural seismicity from broadband seismometers, both onshore and offshore. Moreover, synthetic ground motions are generated to address the paucity of recordings (especially strong motions) in the North Sea region. The associated flat-file, including the metadata and intensity measures (e.g., spectral acceleration and Fourier amplitude) of manually processed waveforms is constructed for the analysis of the ground motion characteristics in the North Sea. An empirical ground-motion model is developed based on the recorded and synthetic data, which is validated and compared with the available observations and models for the North Sea.The ground-motion model is defined for a reference rock condition. Amplification factors to estimate shaking at the soil surface are derived based on a database of one-dimensional site response analyses. The sediments encountered in the North Sea have been deposited in dynamically changing environments ranging from arctic to temperate and reworked by the movement of ice sheets. As a result, a wide range of soil types and properties are found. To capture this variability, representative profiles are developed based on site investigations from locations with different soil conditions encountered in the North Sea. One dimensional non-linear site response analyses are then performed using the recorded and synthetic ground motion database to generate a database of response spectra amplification values.This study presents the preliminary results of the North Sea ground-motion model and highlights the challenges in conducting PSHA for the North Sea region. These results improve the assessment of seismic hazard and risks to CO2 storage security in the North Sea.

In engineering applications, the permanent displacement (D) commonly serves as a useful indicator of the seismic performance of slopes. When developing empirical displacement models as a function of ground-motion intensity measures (IMs), the IMs that are best correlated to D are preferred. On the other hand, the predictability of IMs, in terms of the standard deviations using ground motion models, is also of concern in developing D models. This study aims to: (1) investigate the efficiency of IMs in developing D models for a cohesive-frictional slope based on numerical analysis; and (2) compare the means and standard deviations of randomized D by considering uncertainties in predicting both the IMs and D via Monte Carlo simulation (MCS). A total of 10 scalar IMs and 38 vector-IMs, are employed to develop D models. The results indicate that the spectral acceleration at a degraded period of the soil layer (SA(1.5Ts,layer)) and Arias intensity (IA) are the two most efficient scalar IMs. Additionally, the vector-IMs consisting of [IA, spectrum intensity] and [IA, mean period] are the two most efficient vectors. The MCS results illustrate that the rankings for standard deviations of D models and total standard deviations (i.e., including ground motion variability) may be considerably different. The results are also found to be dependent on earthquake magnitudes and site conditions. This study could provide guidance on the development of numerical-based D models especially within a probabilistic seismic slope displacement analysis framework.KeywordsSeismic slope performanceNumerical analysisIntensity measureDisplacement predictionModel variability

Modelling the spatial correlation of ground motion intensity measures (IMs) has become a keystone in seismic hazard and risk analysis of portfolios of buildings, spatially distributed infrastructures and earthquake-induced phenomena. The quantification of the seismic performance of such systems over a region requires knowledge of the joint probability of occurrence of different ground motion IMs at multiple locations. Therefore, the classical Probabilistic Seismic Hazard Assessment (PSHA) tools, which are based on the hypothesis of independency between IMs at closely spaced sites, are not appropriate. Over the past decade, the spatial correlation of peak ground acceleration (PGA) and spectral acceleration (SA) has been widely studied. Although common findings suggest that the correlation of intra-event residuals decreases quite rapidly with increasing separation distances, these models feature different rates of decay. Among the causes that may lead to inconsistencies between models, with significant impact on hazard and loss estimates, are the multiple techniques used to estimate the correlation structure, the region and local site conditions, as well as the choice of the databases. Furthermore, little effort has been directed towards other IMs suitable to characterize the resulting damage to structures and predict ground failure: peak ground velocity (PGV), peak ground displacement (PGD) and spectral displacement (SD) as well as Arias intensity (퐼") and cumulative absolute velocity (CAV), to name but a few. A proper definition of the seismic action in terms of spectral displacement ordinates has progressively gained importance in performance-based seismic design, and 퐼" and CAV have been found to be adequate for many other earthquake engineering applications, such as evaluating the susceptibility to liquefaction and earthquake-induced landslides. In this study, we use geostatistical tools in order to compute the spatial correlations of such ground motion parameters. We perform comparisons with other existing models with the aim of: (1) identifying factors that most affect the correlation structure, and (2) quantifying the variability of correlation lengths between different events and regions. Moreover, spatial correlation models are usually calibrated on the within-event component of residuals, obtained based on ergodic ground motion prediction equations (GMPEs). Therefore, we also analyse the spatial correlation of event- and site- corrected residuals, retrieved relaxing the ergodic assumption, to further investigate the factors that determine the spatial dependency of IMs. In order to address these issues, we use the 2016-2017 Central Italy seismic sequence database, which includes nine Mw ≥ 5.0 earthquakes that occurred over a time period of five months. These data allow some uncertainties to be removed and an evaluation of the event-to-event variability of the spatial correlation because the same seismic region is considered. Our preliminary results will provide a more accurate picture of ground motions, and thus improve the modelling of earthquake losses for risk model development.

We updated our Next Generation Attenuation (NGA)‐West1 ground motion models (GMMs) for the horizontal components of Arias intensity (AI) and cumulative absolute velocity (CAV) using the functional form and NGA‐West2 database we used to develop GMMs for peak‐amplitude and peak‐spectral ground motion intensity measures (GMIMs). Our results show that CAV has the best goodness‐of‐fit statistics of all the GMIMs we have evaluated up to this time. Its relatively small between‐ and within‐event standard deviations confirm its superior predictability. On the other hand, AI has the highest standard deviation of any GMIM we have studied thus far, which is approximately double that of CAV. Although either CAV or AI or a combination of both have been shown to meet various performance metrics proposed in the context of performance‐based earthquake engineering (PBEE), CAV's high level of predictability makes it superior to AI for use in engineering applications, such as PBEE, that involve probabilistic inference.

Mechanical metamaterials - engineered materials whose behavior is defined by their internal structure rather than their base material - have received great at- tention for the unusual properties they can exhibit. However, while the forward problem of predicting the mechanical behavior of a given metamaterial can be reliably done through simulation or experiments, the inverse problem - designing metamaterials with specific properties - remains difficult, especially for heteroge- neous metamaterials composed of multiple unit cells. This dissertation explores the use of generative machine learning to address this inverse design problem. The first part of the work investigates how inverse and generative models can be conditioned to produce unit cells with prescribed mechanical properties and how they can be used to generate multiple valid solutions for the same target. This is examined using a curved-beam metamaterial, which allows a compact geometric representation without complex design restrictions. The effect these restrictions have on the generative models is investigated in the second part. For this, a number of generative models—Variational Autoencoders, Generative Adversarial Networks, and Diffusion Models—are evaluated on a kirigami metamaterial where dependencies between the cuts cause intricate design constraints. The final part covers the challenges that arise when generative models are applied to heteroge- neous metamaterials, in which multiple unit cells are combined to create spatially varying mechanical properties. The results show that the applicability of generative models for the design of metamaterials strongly depends on the choice of geometric parameterization. Generative models make assumptions about their input data that generally hold for images, but can be invalid for metamaterials when complex dependencies be- tween the input parameters exist. B-splines can provide a representation without those dependencies and are therefore well suited to be paired up with generative models. Furthermore, it is also important how these geometrical parameters are sampled to create the training data for the generative models, as this sampling also affects the distribution of the properties in the training data. Overall, while generative machine learning models prove effective for the inverse design of mechanical metamaterials their successful application requires careful parameterization and selection of the training data.

Iceland is seismically the most active region in northern Europe. Large single earthquakes (~ $$ M_{\text{w}} $$ 7) and seismic sequences of moderate-to-strong earthquakes (~ $$ M_{\text{w}} $$ 6–6.5) have repeatedly occurred during past centuries in the populated South Iceland Seismic Zone (SISZ). The seismic hazard in Iceland has mainly been evaluated using ground motion models (GMMs) developed from strong-motion observations in other countries and only to a very limited extent from Icelandic data, despite a particularly rapid attenuation of ground motions with distance in Iceland. In this study, we evaluate the performance of these GMMs against the Icelandic strong-motion dataset, consisting of peak ground accelerations of moderate-to-strong ( $$ M_{\text{w}} $$ 5–6.5) and local (0–80 km) earthquakes in the SISZ. We find that these GMMs exhibit both a strong bias against the dataset and a relatively large variability, which calls their applicability and earlier hazard analyses into question. To address this issue, we recalibrate each of the GMMs to the dataset using Bayesian regression and Markov Chain Monte Carlo simulations. This approach allows useful prior information of the GMM parameters to be combined with the likelihood of the observed data and provides posterior probability density functions of model residuals and regression parameters. The recalibrated GMMs are unbiased with respect to the data and have a low total standard deviation of around 0.17 (base-10 logarithmic units). The model-to-model variability in the median predictions vary primarily with distance, reaching 0.05 the lowest for $$ M_{\text{w}} $$ 6.3–6.5 at intermediate distances. While the lack of near-fault and far-field data, particularly at large magnitudes, and the different functional forms of the GMMs calibrated to the same dataset may affect the results, the recalibrated GMMs should represent well the ground motions of a typical sequence of moderate-to-strong SISZ earthquakes. We present the recalibrated GMMs of this study as promising candidates for future use in ground motion prediction in Iceland e.g., in the context of either a logic tree or the backbone approach in probabilistic seismic hazard assessment.

Drug discovery is a multi-stage process, often beginning with the identification of active molecules from a high-throughput screen or machine learning model. Once structure activity relationship trends become well established, identifying new analogs with better properties is important. Synthesizing these new compounds is a logical next step, and is key to research groups that have a synthetic chemistry team or external collaborators. Generative machine learning models have become widely adopted to generate new molecules and explore molecular space, with the goal of discovering novel compounds with desires properties. These generative models have been composed from recurrent neural networks (RNNs), Variational Autoencoders (VAEs), and Generative Adversarial Networks (GANs) and are often combined with transfer learning or scoring of physicochemical properties to steer generative design. While these generative models have proven useful in generating new molecular libraries, often they are not capable of addressing a wide variety of potential problems, and often converge into similar molecular space when combined with a scoring function for desired properties. In addition, generated compounds are often not synthetically feasible, reducing their capabilities outside of virtual composition and limiting their usefulness in real-world scenarios. Here we introduce a suite of automated tools called MegaSyn representing 3 components: a new hill-climb algorithm which makes use of SMILES-based RNN generative models, analog generation software, and retrosynthetic analysis coupled with fragment analysis to score molecules for their synthetic feasibility. We now describe the development and testing of this suite of tools and propose how they might be used to optimize molecules or prioritize promising lead compounds using test case examples.

Arias Intensity is a ground motion parameter that captures the potential destructiveness of an earthquake as the integral of the square of the acceleration–time history. It correlates well with several commonly used demand measures of structural performance, liquefaction, and seismic slope stability. A new empirical relationship is developed to estimate Arias Intensity as a function of magnitude, distance, fault mechanism, and site category based on 1208 recorded ground motion data from 75 earthquakes in active plate‐margins. Its functional form is derived from the point‐source model, and the coefficients are determined through non‐linear regression analyses using a random‐effects model. The results show that for large magnitude earthquakes (M > 7) Arias Intensity was significantly overestimated by previous relationships while it was underestimated for smaller magnitude events (M ⩽ 6). The average horizontal Arias Intensity is not significantly affected by forward rupture directivity in the near‐fault region. The aleatory variability associated with Arias Intensity is larger than that of most other ground motion parameters such as spectral acceleration. However, it may be useful in assessing the potential seismic performance of stiff engineering systems whose response is dominated by the short‐period characteristics of ground motions. Copyright © 2003 John Wiley & Sons, Ltd.

High-performance computing (HPC) plays a central role in advancing AI-based approaches for time-critical natural hazard applications, especially in regions where observational data are limited. In seismology, the scarcity of strong-motion records for large earthquakes poses a major challenge for the development of purely data-driven ground motion models. Here, we highlight the use of HPC to generate large, high-fidelity synthetic earthquake datasets specifically tailored for training machine-learning (ML) models for rapid ground motion forecasting in Southern Iceland.Using the CyberShake workflow on HPC systems, we compute an unprecedented ensemble of approximately 100,000 physics-based earthquake scenarios, spanning magnitudes Mw 5.0–7.4, at 350 synthetic stations across the Southern Iceland Seismic Zone and the Reykjanes Peninsula Oblique Rift. Seismic wave propagation is simulated deterministically up to 2 Hz using three alternative Earth velocity models, allowing us to systematically investigate how subsurface velocity heterogeneity influences ground motion. By exploiting seismic reciprocity, the computational cost scales with the number of virtual recording sites rather than with the number of earthquakes, making it feasible to explore tens of thousands of rupture scenarios on Tier-0 HPC systems. The resulting simulations combine multiple velocity models, dense site coverage, and designed magnitude distributions, forming a comprehensive and carefully curated training dataset.This large HPC-generated database is then used to train machine-learning surrogate models within the Machine Learning Estimator for Ground Shaking Maps (MLESmap) framework, including both tree-based ensembles and deep neural networks. Although these ML models provide near-instantaneous predictions of ground motion intensity measures during post-event response, their reliability ultimately depends on the quality, diversity, and physical realism of the underlying training data.Our results show that HPC-driven simulation workflows can effectively close the data gap in regions with limited observations, delivering physically grounded datasets that support robust AI models for time-critical seismic hazard assessment. More broadly, this work underscores the role of HPC not only as a computational tool for modeling extreme events, but as a cornerstone of next-generation AI-driven systems for hazard forecasting and emergency response.

Bottleneck problems are an important class of optimization problems that have recently gained increasing attention in the domain of machine learning and information theory. They are widely used in generative models, fair machine learning algorithms, design of privacy-assuring mechanisms, and appear as information-theoretic performance bounds in various multi-user communication problems. In this work, we propose a general family of optimization problems, termed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">complexity-leakage-utility bottleneck (CLUB)</i> model, which (i) provides a unified theoretical framework that generalizes most of the state-of-the-art literature for the information-theoretic privacy models, (ii) establishes a new interpretation of the popular generative and discriminative models, (iii) constructs new insights for the generative compression models, and (iv) can be used to obtain fair generative models. We first formulate the CLUB model as a complexity-constrained privacy-utility optimization problem. We then connect it with the closely related bottleneck problems, namely information bottleneck (IB), privacy funnel (PF), deterministic IB (DIB), conditional entropy bottleneck (CEB), and conditional PF (CPF). We show that the CLUB model generalizes all these problems as well as most other information-theoretic privacy models. Then, we construct the deep variational CLUB (DVCLUB) models by employing neural networks to parameterize variational approximations of the associated information quantities. Building upon these information quantities, we present unified objectives of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">supervised</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsupervised</i> DVCLUB models. Leveraging the DVCLUB model in an unsupervised setup, we then connect it with state-of-the-art generative models, such as variational auto-encoders (VAEs), generative adversarial networks (GANs), as well as the Wasserstein GAN (WGAN), Wasserstein auto-encoder (WAE), and adversarial auto-encoder (AAE) models through the optimal transport (OT) problem. We then show that the DVCLUB model can also be used in fair representation learning problems, where the goal is to mitigate the undesired bias during the training phase of a machine learning model. We conduct extensive quantitative experiments on colored-MNIST and CelebA datasets.

This article documents the earthquake ground motion database developed for the NGA‐East Project, initiated as part of the Next Generation Attenuation (NGA) research program and led by the Pacific Earthquake Engineering Research Center (PEER). The project was focused on developing a ground motion characterization model (GMC) model for horizontal ground motions for the large region referred to as Central and Eastern North America (CENA). The CENA region covers most of the U.S. and Canada, from the Rocky Mountains to the Atlantic Ocean and is characterized tectonically as a stable continental region (SCR). The ground‐motion database includes the two‐ and three‐component ground‐motion recordings from numerous selected events relevant to CENA ( M &gt; 2.5, with distances up to 3500 km) that have been recorded since 1976. The final database contains over 27,000 time series from 82 earthquakes and 1271 recording stations. The ground motion database includes uniformly processed time series, 5% damped pseudo‐spectral acceleration (PSA) median‐component ordinates for 429 periods ranging from 0.01 to 10 s, duration and Arias intensity in 5% increments, and Fourier amplitude spectra for different time windows. Ground motions and metadata for source, path, and site conditions were subjected to quality checks by topical working groups and the ground‐motion model (GMM) developers. The NGA‐East database constitutes the largest database of processed recorded ground motions in SRCs and is publicly available from the PEER ground‐motion database website.

Accurately characterizing ground motions is crucial for estimating probabilistic seismic hazard and risk. The growing number of ground-motion models, and increased use of simulations in hazard and risk assessments, warrants a comparison between the different techniques available to predict ground motions. This research aims at investigating how the use of different ground-motion models can affect seismic hazard and risk estimates. For this purpose, a case study is considered with a circular seismic source zone and two line sources. A stochastic ground-motion model is used within a Monte Carlo analysis to create a benchmark hazard output. This approach allows the generation of many records, helping to capture details of the ground-motion median and variability, which a ground motion prediction equation may fail to properly model. A variety of ground-motion models are fitted to the simulated ground motion data, with fixed and magnitude-dependant standard deviations (sigmas) considered. These include classic ground motion prediction equations (with basic and more complex functional forms), and a model using an artificial neural network. Hazard is estimated from these models and then we extend the approach to a risk assessment for an inelastic single-degree-of-freedom-system. Only the artificial neural network produces accurate hazard results below an annual frequency of exceedance of 1 × 10–3 years−1. This has a direct impact on risk estimates—with ground motions from large, close-to-site events having more influence on results than expected. Finally, an alternative to ground-motion modelling is explored through an observational-based hazard assessment which uses recorded strong-motions to directly quantify hazard.

The ground motion model (GMM) plays a vital role in the generation of seismic design basis ground motion parameters. Even though many intra-plate GMMs are available, very few of them are based on Peninsular India (PI) region-specific seismological parameters. Hence, it is imperative to develop a GMM using seismological parameters derived from earthquakes in the Peninsular Indian region. In this study, a new GMM is developed for a PI rock site. Due to the scarcity of real earthquakes, artificial earthquake records are simulated to generate a new GMM for PI. The accelerograms of these artificial earthquakes are obtained from the stochastic finite fault simulation technique. Region-specific seismological parameters are obtained from the available PI earthquakes. The generated GMM is compared with other intra-plate GMMs for different earthquake magnitudes. Also, the generated GMM is validated with the Koyna earthquake record and it is observed that the GMM’s predictions are closer to the record.

Ground motion models (GMMs) are a key component in seismic hazard assessment and in seismic risk analysis. The consideration of both aleatory and epistemic sources of variability may have significant influence on the results and are vital because of their influence on the over- or under-estimation of the final assessment of losses. Recent research has shown that the commonly used framework of weighted logic trees for the choice of GMMs is not necessarily the best suited to account for epistemic uncertainty. Recently, a simple and alternative procedure has been proposed in which a GMM suite is defined with only three representative models (lower, central and upper) derived from available median models. This alternative model is equivalent to the use of multiple models, provided the same range of epistemic uncertainty is sampled. The representative suite approach was applied to the European context for developing a Pan-European GMM for EC8 ground type B and normal or strike slip faulting style for its implementation in risk analysis of critical infrastructures Europe wide, within the framework of the European funded project INFRARISK. The proposed new Pan-European representative GMM is based on the most recent GMMs developed using the common RESORCE strong-motion database of European and Near and Middle East acceleration records. It is shown to perform well when tested against new ground-motion observations from the ESM-Engineering Strong-Motion database and even slightly better than other available GMMs. The procedure is efficient and transparent limiting the sample space to three GMMs and reducing both complexity of the modelling and computational efforts.

This study evaluates the Soviet-era ground motion prediction equation (named as A&amp;amp;K-1979) and introduces an Artificial Neural Network (ANN)-based GMM specifically designed for Azerbaijan to improve prediction accuracy. Ground motion models (GMMs) are essential for predicting earthquake-induced ground motions, aiding seismic hazard assessments and engineering designs. While traditional linear empirical models have been widely used, they often struggle to capture complex nonlinear ground motion behaviors. The performance of A&amp;amp;K-1979 was assessed using a strong-motion dataset comprising 500 records collected between 2022 and 2024. Two variants of A&amp;amp;K-1979 were tested: A&amp;amp;K-1979-1 for PGA ≥160 cm/s2 and A&amp;amp;K-1979-2 for PGA &amp;lt;160 cm/s2. An ANN-based GMM was developed using earthquake magnitude and hypocentral distance as inputs, followed by three hidden layers (32-32-16 neurons) with the Rectified Linear Unit (ReLU) activation function. The model was validated with a separate dataset of 268 records, evaluated using metrics such as bias, standard deviation of residuals (σ), mean absolute error (MAE), root mean squared error (RMSE), and R2. The A&amp;amp;K-1979 model exhibited notable prediction biases: A&amp;amp;K-1979-1 overestimated PGA values, while A&amp;amp;K-1979-2 underestimated them. The ANN-based GMM achieved improved performance metrics, with a bias of -0.0076, σ of 0.5971, MAE of 0.4416, RMSE of 0.5972, and an R2 of 0.4601. The improved accuracy of the ANN-based GMM highlights its potential as a valuable tool for seismic hazard assessments in Azerbaijan. By providing enhanced prediction capabilities, the ANN model demonstrates greater reliability and practical value than A&amp;amp;K-1979, reinforcing the need for updated predictive models in the region and supporting its use in preliminary hazard analysis.