Continuous-time Modeling Approach Research Articles

Development and Implementation of Physics-Informed Neural ODE for Dynamics Modeling of a Fixed-Wing Aircraft Under Icing/Fault

Accurate dynamics modeling is crucial for the safety and control of fixed-wing aircraft under perturbation (e.g. icing/fault). In this work, we propose a physics-informed Neural Ordinary Differential Equation (PI-NODE)-based scheme for aircraft dynamics modeling under icing/fault. First, icing accumulation and control surface faults are considered and injected into the nominal (clean) aircraft dynamics model. Second, the physics knowledge of aircraft dynamics modeling is divided into kinematics and kinetics. The former is universally applicable and borrows directly from the nominal aircraft. The latter kinetics knowledge, which hinges on external forces and moments, is inaccurate and challenging under icing/fault. To address this issue, we employ Neural ODE to compensate for the residual between the aircraft dynamics under icing/fault and the nominal (clean) condition, resulting in a naturally continuous-time modeling approach. In experiments, we benchmark the proposed PI-NODE against three baseline methods in a dedicated flight scenario. Comparative studies validate the higher accuracy and improve the generalization ability of the proposed PI-NODE for aircraft dynamics modeling under icing/fault.

Are paranoid ideation and hallucination spectrum experiences differently associated with affect dynamics? A continuous-time modeling approach.

Psychotic experiences have been associated with distortions in affective functioning, including aberrancies in affect dynamics. However, it remains unclear whether the two principal symptom dimensions of psychosis, namely paranoid ideation and hallucination spectrum experiences, are differently associated with affect dynamics, and whether associations hold after statistically controlling for depressive symptoms. We investigate this by using a novel statistical approach, the hierarchical Ornstein-Uhlenbeck (OU) process model. This is a continuous-time stochastic differential equations model in a Bayesian framework that describes dynamics in affective valence and arousal via three core parameters: attractor point, variability, and attractor strength. In a community sample with varying levels of psychotic experiences (n = 116), we measured affective valence and arousal 10 times per day for 7 days, using the experience-sampling method. We found-while statistically controlling for depressive symptoms-credible between-subjects associations between paranoid ideation and attractor points of negative valence and high arousal. We also found a credible positive association between hallucination spectrum experiences and arousal variability. Limited evidence emerged for small associations between paranoid ideation and high valence variability as well as between paranoid ideation and high attractor strengths of valence and arousal. Hallucination spectrum experiences showed some evidence for a small association with high arousal attractor points. The detailed picture of affect dynamics provided by the OU model reveals different cross-sectional affective profiles associated with paranoid ideation versus hallucination spectrum experiences that suggest different affective mechanisms of their formation and maintenance. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Supplemental Material for Are Paranoid Ideation and Hallucination Spectrum Experiences Differently Associated With Affect Dynamics? A Continuous-Time Modeling Approach

Supplemental Material for Are Paranoid Ideation and Hallucination Spectrum Experiences Differently Associated With Affect Dynamics? A Continuous-Time Modeling Approach

Spatio-Temporal Value of Energy Storage in Transmission Networks

This article proposes a continuous-time modeling approach to calculate the spatio-temporal value of energy storage (ES) devices in power transmission networks. More specifically, this article formulates the dynamic operation of ES devices in power transmission networks as a continuous-time optimal control problem, where the Lagrange multiplier trajectories of nodal power balance constraints are defined as continuous-time locational marginal prices (LMPs). In addition, the adjoint functions associated with ES state equations are calculated in closed-form, which define the locational value of stored energy (LVSE) in ES devices. The notion of LVSE is, then, leveraged to define incremental charging utility and discharging cost rates of ES devices, which pass on the spatio-temporal values of ES devices to the continuous-time LMPs. The numerical results of implementing the proposed continuous-time model on a test 3-bus power system and the IEEE-Reliability Test System highlight its effectiveness in calculating the value of ES energy shifting and congestion relief services in transmission networks.

Structural change in the Chicago region and the impact on emission inventories in a continuous-time modeling approach

Motivated by both the need to model recent structural economic changes and the need to understand better the nature of environmental–economic interactions, this paper introduces a continuous-time regional econometric input–output model for the Chicago economy that can be used to analyze, at disaggregated sectoral and temporal levels, the economic and environmental implications of changes exogenous to the economy. The model’s solution yields estimates of emission inventories, which may be used to analyze environmental implications of various economic changes and policy restrictions. This model is the first integrated economic–environmental model of which we are aware that has been formulated and estimated in continuous time for the regional economy of a metropolitan area. We believe that the model’s formulation will enable it to enjoy greater compatibility with natural science-based models, which share such a formulation and flexibility in projecting future emissions corresponding to alternative future economic scenarios and in evaluating emissions policies relevant to such scenarios.

The importance of perceived care and connectedness with friends and parents for adolescent social anxiety.

Nonclinical social anxiety in adolescence can be highly problematic, as it likely affects current and especially new social interactions. Relationships with significant others, such as close friends, mothers, and fathers, could aid socially anxious adolescents' participation in social situations, thereby helping reduce feelings of social anxiety. We examined whether making friends as well as high friendship quality help reduce social anxiety over time, and whether friends', mothers', and fathers' care interact in reducing social anxiety. Using longitudinal data from 2,194 participants in a social network (48% girls; Mage = 13.58) followed for 3 years, we estimated friendship selection and influence processes via a continuous time-modeling approach using SIENA. We controlled for the effects of depressive symptoms, self-esteem, gender, age, and family structure. Our findings suggest that perceived care by friends mediated the effect of making friends on social anxiety. Perceptions of mother and father, as well as friend care and connectedness, respectively, did not interact in decreasing social anxiety. Nonetheless, care and connectedness with mothers, fathers, and friends jointly predicted decreases in social anxiety. Caring relationships with friends and parents each play a role in mutually protecting early adolescents against increasing in social anxiety over time.

On the Continuous-Time Model for Nonlinear-Memory Modeling of RF Power Amplifiers

The RF front-end in modern communication systems is faced with variable envelope and large bandwidth signals (including desired signals and large interferers), which require the behavioral model of the amplifying unit (either in Tx or Rx) to accurately account for nonlinear memory effects. Important advancements have been made on the subject; however it is still challenging to derive a model that performs equally well with all possible input stimuli. This paper gives a concise overview of the recent developments that have been made on the continuous-time modeling approach for the behavioral modeling of nonlinear memory in power amplifiers, as opposed to the explicit discrete-time modeling approach.

Risk sensitive asset allocation

Abstract This paper develops a continuous time modeling approach for making optimal asset allocation decisions. Macroeconomic and financial factors are explicitly modeled as Gaussian stochastic processes which directly affect the mean returns of the assets. We employ methods of risk sensitive control theory, thereby using an infinite horizon objective that is natural and features the long run expected growth rate and the asymptotic variance as two measures of performance, analogous to the mean return and variance, respectively, in the single period Markowitz model. The optimal strategy is a simple function of the factor levels, and, even with constraints on the portfolio proportions, it can be computed by solving a quadratic program. Explicit formulas can be obtained, as is illustrated by an example where the only factor is a Vasicek-type interest rate and where there are two assets: cash and a stock index. The methods are further illustrated by studies of two data sets: U.S. data with two assets and up to three factors, and Australian data with three assets and three factors.

A discrete space continuous time modeling approach to nonsteady flow in a leaky aquifer system of finite configuration

Existing analytical procedures for nonsteady flow in a leaky confined aquifer assume that the aquifer system is areally infinite. A technique is presented that treats a leaky confined aquifer system of finite configuration. By means of a discrete space continuous time (DSCT) modeling approach, the partial differential equation governing the flow system is transformed into a set of ordinary differential equations that can be easily integrated numerically on a high speed digital computer using available scientific subroutines. The finite difference formulation is in effect an explicit scheme. A criterion is developed for which the scheme is computationally stable. A numerical example is presented.