Hybrid modeling and prediction of dynamical systems.
Ontology highlight
ABSTRACT:
SUBMITTER: Hamilton F
PROVIDER: S-EPMC5524426 | biostudies-other | 2017 Jul
REPOSITORIES: biostudies-other
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Project description:Hybrid systems are traditionally difficult to identify and analyse using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics, which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty and characterizes switching behaviour. Specifically, we use the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass-spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviours is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots and the protection of cyber infrastructures.
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Project description:ObjectiveAnhedonia, traditionally defined as a diminished capacity for pleasure, is a core symptom of schizophrenia (SZ). However, modern empirical evidence indicates that hedonic capacity may be intact in SZ and anhedonia may be better conceptualized as an abnormality in the temporal dynamics of emotion.MethodTo test this theory, the current study used ecological momentary assessment (EMA) to examine whether abnormalities in one aspect of the temporal dynamics of emotion, sustained reward responsiveness, were associated with anhedonia. Two experiments were conducted in outpatients diagnosed with SZ (n = 28; n = 102) and healthy controls (n = 28; n = 71) who completed EMA reports of emotional experience at multiple time points in the day over the course of several days. Markov chain analyses were applied to the EMA data to evaluate stochastic dynamic changes in emotional states to determine processes underlying failures in sustained reward responsiveness.ResultsIn both studies, Markov models indicated that SZ had deficits in the ability to sustain positive emotion over time, which resulted from failures in augmentation (ie, the ability to maintain or increase the intensity of positive emotion from time t to t+1) and diminution (ie, when emotions at time t+1 are opposite in valence from emotions at time t, resulting in a decrease in the intensity of positive emotion over time). Furthermore, in both studies, augmentation deficits were associated with anhedonia.ConclusionsThese computational findings clarify how abnormalities in the temporal dynamics of emotion contribute to anhedonia.
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Project description:The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM) regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more significant in regions associated with extreme events, where data is sparse.
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Project description:Like many other types of cancer, colorectal cancer (CRC) develops through multiple pathways of carcinogenesis. This is also true for colorectal carcinogenesis in Lynch syndrome (LS), the most common inherited CRC syndrome. However, a comprehensive understanding of the distribution of these pathways of carcinogenesis, which allows for tailored clinical treatment and even prevention, is still lacking. We suggest a linear dynamical system modeling the evolution of different pathways of colorectal carcinogenesis based on the involved driver mutations. The model consists of different components accounting for independent and dependent mutational processes. We define the driver gene mutation graphs and combine them using the Cartesian graph product. This leads to matrix components built by the Kronecker sum and product of the adjacency matrices of the gene mutation graphs enabling a thorough mathematical analysis and medical interpretation. Using the Kronecker structure, we developed a mathematical model which we applied exemplarily to the three pathways of colorectal carcinogenesis in LS. Beside a pathogenic germline variant in one of the DNA mismatch repair (MMR) genes, driver mutations in APC, CTNNB1, KRAS and TP53 are considered. We exemplarily incorporate mutational dependencies, such as increased point mutation rates after MMR deficiency, and based on recent experimental data, biallelic somatic CTNNB1 mutations as common drivers of LS-associated CRCs. With the model and parameter choice, we obtained simulation results that are in concordance with clinical observations. These include the evolution of MMR-deficient crypts as early precursors in LS carcinogenesis and the influence of variants in MMR genes thereon. The proportions of MMR-deficient and MMR-proficient APC-inactivated crypts as first measure for the distribution among the pathways in LS-associated colorectal carcinogenesis are compatible with clinical observations. The approach provides a modular framework for modeling multiple pathways of carcinogenesis yielding promising results in concordance with clinical observations in LS CRCs.
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Project description:BackgroundUnderstanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.MethodsIn light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.ResultsComputational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.ConclusionOur proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.
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Project description:The sea surface temperature (SST) is an environmental indicator closely related to climate, weather, and atmospheric events worldwide. Its forecasting is essential for supporting the decision of governments and environmental organizations. Literature has shown that single machine learning (ML) models are generally more accurate than traditional statistical models for SST time series modeling. However, the parameters tuning of these ML models is a challenging task, mainly when complex phenomena, such as SST forecasting, are addressed. Issues related to misspecification, overfitting, or underfitting of the ML models can lead to underperforming forecasts. This work proposes using hybrid systems (HS) that combine (ML) models using residual forecasting as an alternative to enhance the performance of SST forecasting. In this context, two types of combinations are evaluated using two ML models: support vector regression (SVR) and long short-term memory (LSTM). The experimental evaluation was performed on three datasets from different regions of the Atlantic Ocean using three well-known measures: mean square error (MSE), mean absolute percentage error (MAPE), and mean absolute error (MAE). The best HS based on SVR improved the MSE value for each analyzed series by [Formula: see text], [Formula: see text], and [Formula: see text] compared to its respective single model. The HS employing the LSTM improved [Formula: see text], [Formula: see text], and [Formula: see text] concerning the single LSTM model. Compared to literature approaches, at least one version of HS attained higher accuracy than statistical and ML models in all study cases. In particular, the nonlinear combination of the ML models obtained the best performance among the proposed HS versions.
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