New Class Of Models Research Articles

Deep neural helmholtz operators for 3D elastic wave propagation and inversion

Summary Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a Helmholtz neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.

Fixed lines in four fermion models in two dimensions

Motivated by conjectures about near-horizon dynamics in quantum gravity, we search for lines of perturbatively accessible fixed points emanating from models of N free fermions. Through two loops we find a new class of models, apart from the well-known Abelian Thirring models. Further study is needed to see whether these can lead to true conformal manifolds, or perhaps a new class of large-N fixed points. Published by the American Physical Society 2024

Mbtransfer: Microbiome intervention analysis using transfer functions and mirror statistics.

Time series studies of microbiome interventions provide valuable data about microbial ecosystem structure. Unfortunately, existing models of microbial community dynamics have limited temporal memory and expressivity, relying on Markov or linearity assumptions. To address this, we introduce a new class of models based on transfer functions. These models learn impulse responses, capturing the potentially delayed effects of environmental changes on the microbial community. This allows us to simulate trajectories under hypothetical interventions and select significantly perturbed taxa with False Discovery Rate guarantees. Through simulations, we show that our approach effectively reduces forecasting errors compared to strong baselines and accurately pinpoints taxa of interest. Our case studies highlight the interpretability of the resulting differential response trajectories. An R package, mbtransfer, and notebooks to replicate the simulation and case studies are provided.

Max-convolution processes with random shape indicator kernels

In this paper, we introduce a new class of models for spatial data obtained from max-convolution processes based on indicator kernels with random shape. We show that these models have appealing dependence properties including tail dependence at short distances and independence at long distances. We further consider max-convolutions between such processes and processes with tail independence, in order to separately control the bulk and tail dependence behaviors, and to increase flexibility of the model at longer distances, in particular, to capture intermediate tail dependence. We show how parameters can be estimated using a weighted pairwise likelihood approach, and we conduct an extensive simulation study to show that the proposed inference approach is feasible in relatively high dimensions and it yields accurate parameter estimates in most cases. We apply the proposed methodology to analyze daily temperature maxima measured at 100 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.

Hierarchical modeling of irregularly spaced financial returns

Volatility modeling is crucial in finance, especially when dealing with intraday transaction‐level asset returns. The irregular and high‐frequency nature of the data presents unique challenges. While stochastic volatility (SV) models are widely used for understanding patterns in volatility of daily stock returns which constitute regularly spaced time series, new classes of models must be introduced for analyzing volatility in irregularly spaced intraday data. Specifically these models must accommodate the random gaps between successive transactional events. By modeling the gaps using autoregressive conditional duration (ACD) models, we describe a hierarchical irregular SV autoregressive conditional duration (IR‐SV‐ACD) model for estimating and forecasting intertransaction gaps and the volatility of log‐returns. We carry out the analysis in the Bayesian framework via the Hamiltonian Monte Carlo (HMC) algorithm with No‐U‐turn sampler (NUTS) in R using the cmdstanr package. The fits and forecasts are obtained using Monte Carlo averages based on the posterior samples. We illustrate this approach using simulation studies and real data analysis for intraday prices available at microseconds level of health stocks traded on the New York Stock Exchange (NYSE). The log‐returns and gaps are calculated for the stocks and are used for modeling.

Sequencing Initial Conditions in Physics-Informed Neural Networks

The scientific machine learning (SciML) field has introduced a new class of models called physics-informed neural networks (PINNs). These models incorporate domain-specific knowledge as soft constraints on a loss function and use machine learning techniques to train the model. Although PINN models have shown promising results for simple problems, they are prone to failure when moderate level of complexities are added to the problems. We demonstrate that the existing baseline models, in particular PINN and evolutionary sampling (Evo), are unable to capture the solution to differential equations with convection, reaction, and diffusion operators when the imposed initial condition is non-trivial. We then propose a promising solution to address these types of failure modes. This approach involves coupling Curriculum learning with the baseline models, where the network first trains on PDEs with simple initial conditions and is progressively exposed to more complex initial conditions. Our results show that we can reduce the error by 1 – 2 orders of magnitude with our proposed method compared to regular PINN and Evo.

Switched max-plus linear-dual inequalities: cycle time analysis and applications

AbstractP-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.

Diffusion models for out-of-distribution detection in digital pathology

The ability to detect anomalies, i.e. anything not seen during training or out-of-distribution (OOD), in medical imaging applications is essential for successfully deploying machine learning systems. Filtering out OOD data using unsupervised learning is especially promising because it does not require costly annotations. A new class of models called AnoDDPMs, based on denoising diffusion probabilistic models (DDPMs), has recently achieved significant progress in unsupervised OOD detection. This work provides a benchmark for unsupervised OOD detection methods in digital pathology. By leveraging fast sampling techniques, we apply AnoDDPM on a large enough scale for whole-slide image analysis on the complete test set of the Camelyon16 challenge. Based on ROC analysis, we show that AnoDDPMs can detect OOD data with an AUC of up to 94.13 and 86.93 on two patch-level OOD detection tasks, outperforming the other unsupervised methods. We observe that AnoDDPMs alter the semantic properties of inputs, replacing anomalous data with more benign-looking tissue. Furthermore, we highlight the flexibility of AnoDDPM towards different information bottlenecks by evaluating reconstruction errors for inputs with different signal-to-noise ratios. While there is still a significant performance gap with fully supervised learning, AnoDDPMs show considerable promise in the field of OOD detection in digital pathology.

Going Deep in Diagnostic Modeling: Deep Cognitive Diagnostic Models (DeepCDMs).

Cognitive diagnostic models (CDMs) are discrete latent variable models popular in educational and psychological measurement. In this work, motivated by the advantages of deep generative modeling and by identifiability considerations, we propose a new family of DeepCDMs, to hunt for deep discrete diagnostic information. The new class of models enjoys nice properties of identifiability, parsimony, and interpretability. Mathematically, DeepCDMs are entirely identifiable, including even fully exploratory settings and allowing to uniquely identify the parameters and discrete loading structures (the " -matrices") at all different depths in the generative model. Statistically, DeepCDMs are parsimonious, because they can use a relatively small number of parameters to expressively model data thanks to the depth. Practically, DeepCDMs are interpretable, because the shrinking-ladder-shaped deep architecture can capture cognitive concepts and provide multi-granularity skill diagnoses from coarse to fine grained and from high level to detailed. For identifiability, we establish transparent identifiability conditions for various DeepCDMs. Our conditions impose intuitive constraints on the structures of the multiple -matrices and inspire a generative graph with increasingly smaller latent layers when going deeper. For estimation and computation, we focus on the confirmatory setting with known -matrices and develop Bayesian formulations and efficient Gibbs sampling algorithms. Simulation studies and an application to the TIMSS 2019 math assessment data demonstrate the usefulness of the proposed methodology.

Approximate Deconvolution with Correction – A High Fidelity Model for Magnetohydrodynamic Flows at High Reynolds and Magnetic Reynolds Numbers

Abstract We propose a model for magnetohydrodynamic flows at high Reynolds and magnetic Reynolds numbers. The system is written in the Elsässer variables so that the decoupling method of [C. Trenchea, Unconditional stability of a partitioned IMEX method for magnetohydrodynamic flows, Appl. Math. Lett. 27 (2014), 97–100] can be used. This decoupling method is only first-order accurate, so the proposed model aims at improving the temporal accuracy (from first to second order), as well as reducing the modeling error of the existing turbulence model. This is done in the framework of the recently developed LES-C turbulence models [A. E. Labovsky, Approximate deconvolution with correction: A member of a new class of models for high Reynolds number flows, SIAM J. Numer. Anal. 58 (2020), 5, 3068–3090]. We show the model to be unconditionally stable and numerically verify its superiority over its most natural competitor.

Some comments on “A Hermite spline approach for modelling population mortality” by Tang, Li & Tickle (2022)

AbstractTang et al. (2022) propose a new class of models for stochastic mortality modelling using Hermite splines. There are four useful features of this class that are worth emphasising. First, for single-sex datasets, this new class of projection models can be fitted as a generalised linear model. Second, these models can automatically extrapolate mortality rates to ages above the maximum age of the data set. Third, simpler sub-variants of the models exist for forecasting when one of the variables lacks a clear drift. Finally, a minor reparameterisation increases the quality of long-range forecasts of period mortality.

From axion quality and naturalness problems to a high-quality ZN QCD relaxion

We highlight general issues associated with quality and naturalness problems in theories of light QCD-axions, axion-like particles, and relaxions. We show the presence of Planck-suppressed operators generically lead to scalar coupling of axions with the Standard model. We present a new class of $\mathbb Z_{N}$ QCD relaxion models that can address both the QCD relaxion CP problem as well as its quality problem. This new class of models also leads to interesting experimental signatures, which can be searched for at the precision frontier.

DirectVoxGO++: Grid-based fast object reconstruction using radiance fields

In recent years, the computer vision and computer graphics communities have seen the emergence of new classes of models for representing objects based on Neural Radiance Fields (NeRFs). These techniques use ideas based on traditional methods from computer graphics, for example, radiance fields, and combine them with implicit neural representations and neural image-based rendering (IBR). However, one significant drawback of this class of techniques was that they were too slow, taking in the range of hours in high-end GPUs. Due to these limitations, new techniques have been created for the fast reconstruction of scenes, such as Direct Voxel Grid Optimization (DirectVoxGO). Alongside this limitation, initially, NeRFs had limited compositing and modeling capabilities. For example, a simple task such as separating the background from the foreground could not be modeled with NeRFs until the emergence of new techniques such as NeRF++. Our method extends DirectVoxGO to allow the handling of unbounded scenes inspired by some ideas from NeRF++ and also adapts it to incorporate elements from a neural hashing approach employed by other works. Our technique improved photorealism compared with DirectVoxGO and Plenoxels on a subset of the Light Field Dataset on average in at least 2%, 8%, and 8% for Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) metrics, respectively, while also being an order of magnitude faster than NeRF++. Also, we demonstrate that, for the evaluated scenes, our technique has comparable training time and memory consumption than previous works. Code is available in https://github.com/danperazzo/dvgoplusplus.

An integrated estimation approach to incorporate latent variables through SEM into discrete mode choice models to analyze mode choice attitude of a rider

Mode Choice preference of each individual commuter depends on a number of factors. The classic models for choice estimation have majorly focused on the quantifiable variables such as travel cost, travel time, socio-economic characteristics of riders, trip characteristics, and mode characteristics. This paper aims at analyzing the hidden impact of latent variables integrated with observed variables on mode choice attitude of a rider for an integrated public transport system with environment-friendly feeder mode. The study is in a tier II type metropolitan city of Vadodara, Gujarat. For the purpose a new class of model, Integrated Choice and Latent Variable (ICLV) model is introduced. It integrates the Structural Equation Modelling (SEM) through Analysis of Moment Structures (AMOS) approach for the analysis of latent variable with the classic type choice model analyzed through Biogeme regression. The study precisely captures the attitude of a rider towards the need for comfort and convenience, safety and security, services and facilities, and riding attraction and quality class of latent variables. 26 of initially considered 41 latent variables clubbed into four latent constructs through Confirmatory Factor Analysis (CFA) and SEM approach were incorporated in the ICLV analysis. The results explain the riders’ attitude driven choice for comfort and convenience and service and facilities over the safety and security and riding quality aspects of the mode. The shift demand governed by these latent variables helps to develop a methodological framework, which sets up a base for transport system design oriented policies’ implications as future scope of the research.

The generalized doubling method: (𝑘,𝑐) models

One of the key ingredients in the recent construction of the generalized doubling method is a new class of models, called ( k , c ) (k,c) models, for local components of generalized Speh representations. We construct a family of ( k , c ) (k,c) representations, in a purely local setting, and discuss their realizations using inductive formulas. Our main result is a uniqueness theorem which is essential for the proof that the generalized doubling integral is Eulerian.

Estimating MS-BLGARCH Models Using Recursive Method

In this paper a new class of models is proposed for modeling nonlinear and stationary time series. This new class of models is referred to as the Markov-switching bilinear GARCH (MS-BLGARCH) models. In these models, the parameters are allowed to depend on an unobservable time-homogeneous and stationary Markov chain with finite state space. The statistical inference for these models is rather difficult due to the dependence on the whole regime path. We propose a recursive algorithm for parameter estimation in MS − BLGARCH. The proposed method is useful for long time series as well as for data available in real time. The main idea is to use the maximum likelihood estimation (MLE) method and from this develop a recursive Expectation-Maximization (EM) algorithm.

Point estimate observers: A new class of models for perceptual decision making.

Bayesian optimal inference is often heralded as a principled, general framework for human perception. However, optimal inference requires integration over all possible world states, which quickly becomes intractable in complex real-world settings. Additionally, deviations from optimal inference have been observed in human decisions. A number of approximation methods have previously been suggested, such as sampling methods. In this study, we additionally propose point estimate observers, which evaluate only a single best estimate of the world state per response category. We compare the predicted behavior of these model observers to human decisions in five perceptual categorization tasks. Compared to the Bayesian observer, the point estimate observer loses decisively in one task, ties in two and wins in two tasks. Two sampling observers also improve upon the Bayesian observer, but in a different set of tasks. Thus, none of the existing general observer models appears to fit human perceptual decisions in all situations, but the point estimate observer is competitive with other observer models and may provide another stepping stone for future model development. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Transaction time models in multi-state life insurance

ABSTRACT In life insurance contracts, benefits and premiums are typically paid contingent on the biometric state of the insured. Due to delays between the occurrence, reporting, and settlement of changes to the biometric state, the state process is not fully observable in real-time. This fact implies that the classic multi-state models for the biometric state of the insured are not able to describe the development of the policy in real-time, which encompasses handling of incurred-but-not-reported and reported-but-not-settled claims. We give a fundamental treatment of the problem in the setting of continuous-time multi-state life insurance by introducing a new class of models: transaction time models. The relation between the transaction time model and the classic model is studied and a result linking the present values in the two models is derived. The results and their practical implications are illustrated for disability coverages, where we obtain explicit expressions for the transaction time reserve in specific models.

Social order statistics models for ranking data with analysis of preferences in social networks

In the National Longitudinal Study of Adolescent to Adult Health (Add Health) in the United States during the 1994–95 school year, sampled high school students were asked to rank 17 romantic relationship activities in ideal chronological order and to nominate up to five male and five female best friends within the school. It is natural to see that the students’ rank-order progression of social, romantic and sexual relationships may be influenced strongly by their peers or friends. So far, traditional ranking models do not account for such social network dependency. In this article we introduce a new class of models, called social order statistics (SOS) models, to learn ranking data in social networks. The new models combine the order statistics models and spatial autoregressive models to account for social dependencies among the individuals. A flexible formulation of weight matrices in the spatial model is adopted to provide diverse network effects among the individuals for different items. Efficient and scalable MCMC algorithms are developed to perform Bayesian inference in a parallel manner for large networks with even a few thousand nodes. Analysis of the Add Health dataset reveals that social network effects are different for students’ preferences toward different activities in a relationship. In particular, students’ preferences on romantic and sexual events generally have stronger peer effects than those on social events, and opinions of close friends of the same gender tend to have a larger impact on the preferences on sexual events.

Justification of environmental and economic mechanisms of adaptation of agricultural production and rural areas to climate changes

In the course of the research, an analysis of the theoretical basis of the economic-mathematical modeling of the production of agricultural crops depending on the climatic zones and their changes was made. It was established that the ultimate goal of economic-mathematical modeling is the establishment of dependencies between the components of the model, their qualitative and, if possible, quantitative characteristics. Understanding the interrelationships and interdependencies of certain social phenomena and situations makes it possible to choose the relevant tools of state or social influence. Regulation, as the process of influencing the economic or social system, involves the use of a set of administrative, economic and institutional tools. It was determined that when choosing models that allow taking into account the interdependence of socio-economic and climatic phenomena, it is expedient to adapt the existing models to the solution of the researched problems and/or create a new class of models. The correct interdependencies of socio-economic and climatic phenomena were established and their qualitative assessment was carried out. Recommendations have been developed for the use of tools capable of influencing in a given direction the establishment of interrelationships and dependencies when applying a specific climate change assessment model, in particular in the agricultural sector. It is also determined that the models of adaptation of agricultural production to climate changes should be based on the analysis of actual climate changes in the region and the country.