Calibration of a complex hydro-ecological model through Approximate Bayesian Computation and Random Forest combined with sensitivity analysis

An automated calibration method is proposed and applied to the complex hydro-ecological model Delft3D-BLOOM which is calibrated from monitoring data of the lake Champs-sur-Marne, a small shallow urban lake in the Paris region (France). This method (ABC-RF-SA) combines Approximate Bayesian Computation (ABC) with the machine learning algorithm Random Forest (RF) and a Sensitivity Analysis (SA) of the model parameters. Three target variables are used (total chlorophyll, cyanobacteria and dissolved oxygen concentration) to calibrate 133 parameters. ABC-RF-SA is first applied on a set of simulated observations to validate the methodology. It is then applied on a real set of high-frequency observations recorded during about two weeks on the lake Champs-sur-Marne. The methodology is also compared to standard ABC and ABC-RF formulations. Only ABC-RF-SA allowed the model to reproduce the observed biogeochemical dynamics. The coupling of ABC with RF and SA thus appears crucial for its application to complex hydro-ecological models.     

A machine-learning approach to calibrate generic Raman models for real-time monitoring of cell culture processes

The manufacture of biotherapeutic proteins consists of complex upstream unit operations requiring multiple raw materials, analytical techniques, and control strategies to produce safe and consistent products for patients. Raman spectroscopy is a ubiquitous multipurpose analytical technique in biopharmaceutical manufacturing for real-time predictions of critical parameters in cell culture processes. The accuracy of Raman spectroscopy relies on chemometric models that need to be carefully calibrated. The existing calibration procedure is nontrivial to implement as it necessitates executing multiple carefully designed experiments for generating relevant calibration sets. Further, existing procedure yields calibration models that are reliable only in operating conditions they were calibrated in. This creates a unique challenge in clinical manufacturing where products have limited production history. In this paper, a novel machine-learning procedure based on just-in-time learning (JITL) is proposed to calibrate Raman models. Unlike traditional techniques, JITL-based generic Raman models can be reliably used for different modalities, cell lines, culture media, and operating conditions. The accuracy of JITL-based generic models is demonstrated on several validation studies involving real-time predictions of critical cell culture performance parameters, such as glucose, glutamate, glutamine, ammonium, lactate, sodium, calcium, viability, and viable cell density. The proposed JITL framework introduces a paradigm shift in the way industrial Raman models are calibrated, which to the best of authors’ knowledge have not been done before.     

Microbial models with data‐driven parameters predict stronger soil carbon responses to climate change

Long‐term carbon (C) cycle feedbacks to climate depend on the future dynamics of soil organic carbon (SOC). Current models show low predictive accuracy at simulating contemporary SOC pools, which can be improved through parameter estimation. However, major uncertainty remains in global soil responses to climate change, particularly uncertainty in how the activity of soil microbial communities will respond. To date, the role of microbes in SOC dynamics has been implicitly described by decay rate constants in most conventional global carbon cycle models. Explicitly including microbial biomass dynamics into C cycle model formulations has shown potential to improve model predictive performance when assessed against global SOC databases. This study aimed to data‐constrained parameters of two soil microbial models, evaluate the improvements in performance of those calibrated models in predicting contemporary carbon stocks, and compare the SOC responses to climate change and their uncertainties between microbial and conventional models. Microbial models with calibrated parameters explained 51% of variability in the observed total SOC, whereas a calibrated conventional model explained 41%. The microbial models, when forced with climate and soil carbon input predictions from the 5th Coupled Model Intercomparison Project (CMIP5), produced stronger soil C responses to 95 years of climate change than any of the 11 CMIP5 models. The calibrated microbial models predicted between 8% (2‐pool model) and 11% (4‐pool model) soil C losses compared with CMIP5 model projections which ranged from a 7% loss to a 22.6% gain. Lastly, we observed unrealistic oscillatory SOC dynamics in the 2‐pool microbial model. The 4‐pool model also produced oscillations, but they were less prominent and could be avoided, depending on the parameter values.     

Scaling from mycelial growth to infection dynamics: a reaction diffusion approach

Numerous models have been proposed for the dynamics of fungal growth, and also for the dynamics of infection. Few models, however, have combined the mechanistic interpretation of mycelial growth with epidemiological models for the transmission of infection. Many of the mechanistic models seek to include considerable biological detail, which necessarily leads to a proliferation of state variables and parameters. Including such models within an epidemiological framework makes interpretation of underpinning processes difficult. A simple reaction diffusion model for the growth and spread of fungal mycelium is introduced and analysed, scaling from the small-scale parameters for mycelial dynamics to the large-scale properties of the colony. By coupling the output to a parsimonious epidemiological model for the dynamics of primary infection, we analyse the sensitivity of the probability of successful infection of a host to the colony dynamics associated with local bulking-up, extension, growth and nutrient consumption by the mycelium. In particular we identify optimal trade-offs in bulking-up versus dispersal in controlling infection dynamics.     

Characterising model dynamics using sparse grid interpolation: Parameter estimation of cholera

Sparse grid interpolation is a popular numerical discretization technique for the treatment of high dimensional, multivariate problems. We consider the case of using time-series data to calibrate epidemiological models from both phenomenological and mechanistic perspectives using this computational tool. By capturing the dynamics underlying both global and local spaces, our algorithm identifies potentially optimal regions of the parameter space and directs computational effort towards resolving the dynamics and resulting fits of these regions. We demonstrate how sparse grid interpolants can be effectively deployed to fit available data and discriminate between competing hypotheses to explain the current cholera epidemic in Yemen.     

An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City

Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time the pandemic lasts. However, often the available data are not sufficient to identify the model parameters and hence infer the unobserved dynamics. Here, we develop a general framework for building a trustworthy data-driven epidemiological model, consisting of a workflow that integrates data acquisition and event timeline, model development, identifiability analysis, sensitivity analysis, model calibration, model robustness analysis, and projection with uncertainties in different scenarios. In particular, we apply this framework to propose a modified susceptible–exposed–infectious–recovered (SEIR) model, including new compartments and model vaccination in order to project the transmission dynamics of COVID-19 in New York City (NYC). We find that we can uniquely estimate the model parameters and accurately project the daily new infection cases, hospitalizations, and deaths, in agreement with the available data from NYC’s government’s website. In addition, we employ the calibrated data-driven model to study the effects of vaccination and timing of reopening indoor dining in NYC.     

基于实码遗传算法的湖泊水质模型参数优化

参数的合理取值决定着模型的模拟效果,因此确定研究区域的模型结构后,需要对模型的参数进行优化.湖泊水质模型(Simulation by means of an Analytical Lake Model,SALMO)利用常微分方程描述湖泊的营养物质循环和食物链动态,考虑了多个生态过程,包含104个参数.由于参数较多,不适宜采用传统参数优化方法进行优化.利用太湖梅梁湾2005年数据,采用实码遗传算法优化了SALMO模型中相对敏感的参数,运用优化后的模型,模拟了梅梁湾2006年的水质.对比分析参数优化前后模型的效果表明遗传算法能高效地对SALMO进行参数优化,优化后的模拟精度得到了显著提高,能更好地模拟梅梁湾的水质变化.     

A general kinetic model for biological nutrient removal activated sludge systems: model evaluation

Hu et al. (2007) presented a general kinetic model for biological nutrient removal (BNR) activated sludge (AS) systems in general, but for external nitrification (EN) BNRAS (ENBNRAS) systems in particular. In this article, this model is evaluated against a large number of experimental data sets. In this evaluation, the model is first used to simulate a wide variety of conventional internal nitrification (IN) BNRAS systems to evaluate its predictions and also evaluate the model parameters suggested by Hu et al. (2007), and to calibrate those constants for which values are not available in the literature. Simulation results indicate that the model, with appropriately calibrated parameters, is capable of predicting COD removal, nitrification and denitrification and two types of biological excess phosphorus removal (BEPR), namely aerobic and anoxic/aerobic P uptake BEPR. The model is then used to simulate the ENBNRAS systems to evaluate its capacity of simulating the behaviour of this system. Simulation results show that the model is capable of simulating the behaviour of the ENBNRAS systems, including COD, nitrification, denitrification and BEPR, particularly anoxic P uptake BEPR, with the values of kinetic and stoichiometric parameters obtained in modelling conventional BNRAS systems, except for micro(NIT), K(MP), eta(PAO) and eta(H) which required calibration.     

Hierarchy of individual calibration levels for heart rate and accelerometry to measure physical activity.

Combining accelerometry with heart rate (HR) monitoring may improve precision of physical activity measurement. Considerable variation exists in the relationships between physical activity intensity (PAI) and HR and accelerometry, which may be reduced by individual calibration. However, individual calibration limits feasibility of these techniques in population studies, and less burdensome, yet valid, methods of calibration are required. We aimed to evaluate the precision of different individual calibration procedures against a reference calibration procedure: a ramped treadmill walking-running test with continuous measurement of PAI by indirect calorimetry in 26 women and 25 men [mean (SD): 35 (9) yr, 1.69 (0.10) m, 70 (14) kg]. Acceleration (along the longitudinal axis of the trunk) and HR were measured simultaneously. Alternative calibration procedures included treadmill testing without calorimetry, submaximal step and walk tests with and without calorimetry, and nonexercise calibration using sleeping HR and gender. Reference accelerometry and HR models explained >95% of the between-individual variance in PAI (P < 0.001). This fraction dropped to 73 and 81%, respectively, for accelerometry and HR models calibrated with treadmill tests without calorimetry. Step-test calibration captured 62-64% (accelerometry) and 68% (HR) of the variance between individuals. Corresponding values were 63-76% and 59-61% for walk-test calibration. There was only little benefit of including calorimetry during step and walk calibration for HR models. Nonexercise calibration procedures explained 54% (accelerometry) and 30% (HR) of the between-individual variance. In conclusion, a substantial proportion of the between-individual variance in relationships between PAI, accelerometry, and HR is captured with simple calibration procedures, feasible for use in epidemiological studies.     

Modeling for Understanding v. Modeling for Numbers

I draw a distinction between Modeling for Numbers, which aims to address how much, when, and where questions, and Modeling for Understanding, which aims to address how and why questions. For-numbers models are often empirical, which can be more accurate than their mechanistic analogues as long as they are well calibrated and predictions are made within the domain of the calibration data. To extrapolate beyond the domain of available system-level data, for-numbers models should be mechanistic, relying on the ability to calibrate to the system components even if it is not possible to calibrate to the system itself. However, development of a mechanistic model that is reliable depends on an adequate understanding of the system. This understanding is best advanced using a for-understanding modeling approach. To address how and why questions, for-understanding models have to be mechanistic. The best of these for-understanding models are focused on specific questions, stripped of extraneous detail, and elegantly simple. Once the mechanisms are well understood, one can then decide if the benefits of incorporating the mechanism in a for-numbers model is worth the added complexity and the uncertainty associated with estimating the additional model parameters.     

基于Penman-Monteith模型的两个蒸散模型在夏玉米农田的参数修正及性能评价

利用涡度相关系统和小气象系统对2013—2015年夏玉米生长季的蒸散量和气象数据进行实时观测,基于观测数据对以Penman-Monteith模型为基础的FAO-PM模型和KP-PM模型进行分析:首先利用2013和2014年数据对两个模型中的关键参数进行校正,其次利用两个模型对2015年夏玉米农田的日蒸散量进行计算,并与测量值对比,说明两个模型在夏玉米农田的适用性;最后采用分阶段法对KP-PM模型中的经验系数进行修正.结果表明: FAO-PM模型对2015年夏玉米农田日蒸散量的计算值更加接近测量值;利用分阶段法对KP-PM模型进行修正后,模型对日蒸散量的计算效果有了很大提高,且计算值比FAO-PM模型更接近测量值.模型中关键系数与气象条件之间有很大关系,因此利用模型进行蒸散预测时,必须先对模型进行参数校正.该研究可为其他研究人员利用模型估算蒸散量提供方法上的参考.     

Modeling the Values of Net Primary Production for the Zonal Vegetation of European Russia

Several modern approaches to the problem of estimating the net primary production of terrestrial ecosystems are discussed. A method for predicting the dynamics of this parameter as a function of radiation balance and annual evapotranspiration is described. The values of annual carbon by the zonal vegetation of European Russia are calculated in two ways: by methods based on the empirically determined relationships between the annual average values of climatic parameters and net primary production and on the basis of models describing carbon flows between the compartments of ecosystems. The model estimations of net primary production are compared with experimental data.     

Construction of robust dynamic genome-scale metabolic model structures of Saccharomyces cerevisiae through iterative re-parameterization

Dynamic flux balance analysis (dFBA) has been widely employed in metabolic engineering to predict the effect of genetic modifications and environmental conditions in the cell׳s metabolism during dynamic cultures. However, the importance of the model parameters used in these methodologies has not been properly addressed. Here, we present a novel and simple procedure to identify dFBA parameters that are relevant for model calibration. The procedure uses metaheuristic optimization and pre/post-regression diagnostics, fixing iteratively the model parameters that do not have a significant role. We evaluated this protocol in a Saccharomyces cerevisiae dFBA framework calibrated for aerobic fed-batch and anaerobic batch cultivations. The model structures achieved have only significant, sensitive and uncorrelated parameters and are able to calibrate different experimental data. We show that consumption, suboptimal growth and production rates are more useful for calibrating dynamic S. cerevisiae metabolic models than Boolean gene expression rules, biomass requirements and ATP maintenance.     

Neutral assembly of bacterial communities

Two recent, independent advances in ecology have generated interest and controversy: the development of neutral community models (NCMs) and the extension of biogeographical relationships into the microbial world. Here these two advances are linked by predicting an observed microbial taxa-volume relationship using an NCM and provide the strongest evidence so far for neutral community assembly in any group of organisms, macro or micro. Previously, NCMs have only ever been fitted using species-abundance distributions of macroorganisms at a single site or at one scale and parameter values have been calibrated on a case-by-case basis. Because NCMs predict a malleable two-parameter taxa-abundance distribution, this is a weak test of neutral community assembly and, hence, of the predictive power of NCMs. Here the two parameters of an NCM are calibrated using the taxa-abundance distribution observed in a small waterborne bacterial community housed in a bark-lined tree-hole in a beech tree. Using these parameters, unchanged, the taxa-abundance distributions and taxa-volume relationship observed in 26 other beech tree communities whose sizes span three orders of magnitude could be predicted. In doing so, a simple quantitative ecological mechanism to explain observations in microbial ecology is simultaneously offered and the predictive power of NCMs is demonstrated.     

Dealing with Uncertainty in Spatially Explicit Population Models

It has been argued that spatially explicit population models (SEPMs) cannot provide reliable guidance for conservation biology because of the difficulty of obtaining direct estimates for their demographic and dispersal parameters and because of error propagation. We argue that appropriate model calibration procedures can access additional sources of information, compensating the lack of direct parameter estimates. Our objective is to show how model calibration using population-level data can facilitate the construction of SEPMs that produce reliable predictions for conservation even when direct parameter estimates are inadequate. We constructed a spatially explicit and individual-based population model for the dynamics of brown bears (Ursus arctos) after a reintroduction program in Austria. To calibrate the model we developed a procedure that compared the simulated population dynamics with distinct features of the known population dynamics (=patterns). This procedure detected model parameterizations that did not reproduce the known dynamics. Global sensitivity analysis of the uncalibrated model revealed high uncertainty in most model predictions due to large parameter uncertainties (coefficients of variation CV 0.8). However, the calibrated model yielded predictions with considerably reduced uncertainty (CV 0.2). A pattern or a combination of various patterns that embed information on the entire model dynamics can reduce the uncertainty in model predictions, and the application of different patterns with high information content yields the same model predictions. In contrast, a pattern that does not embed information on the entire population dynamics (e.g., bear observations taken from sub-areas of the study area) does not reduce uncertainty in model predictions. Because population-level data for defining (multiple) patterns are often available, our approach could be applied widely.     

Modeling daily chlorophyll a dynamics in a German lowland river using artificial neural networks and multiple linear regression approaches

Phytoplankton biomass is an important indicator for water quality, and predicting its dynamics is thus regarded as one of the important issues in the domain of river ecology and management. However, the vast majority of models in river systems have focused mostly on flow prediction and water quality with very few applications to biotic parameters such as chlorophyll a (Chl a). Based on a 1.5-year measured dataset of Chl a and environmental variables, we developed two modeling approaches [artificial neural networks (ANN) and multiple linear regression (MLR)] to simulate the daily Chl a dynamics in a German lowland river. In general, the developed ANN and MLR models achieved satisfactory accuracy in predicting daily dynamics of Chl a concentrations. Although some peaks and lows were not predicted, the predicted and the observed data matched closely by the MLR model with the coefficient of determination (R ²), Nash–Sutcliffe efficiency (NS), and the root mean square error (RMSE) of 0.53, 0.53, and 2.75 for the calibration period and 0.63, 0.62, and 1.94 for the validation period, respectively. Likewise, the results of the ANN model also illustrated a good agreement between observed and predicted data during calibration and validation periods, which was demonstrated by R ², NS, and RMSE values (0.68, 0.68, and 2.27 for the calibration period, 0.55, 0.66 and 2.12 for the validation period, respectively). According to the sensitivity analysis, Chl a concentration was highly sensitive to dissolved inorganic nitrogen, nitrate–nitrogen, autoregressive Chl a, chloride, sulfate, and total phosphorus. We concluded that it was possible to predict the daily Chl a dynamics in the German lowland river based on relevant environmental factors using either ANN or MLR models. The ANN model is well suited for solving non-linear and complex problems, while the MLR model can explicitly explore the coefficients between independent and dependent variables. Further studies are still needed to improve the accuracy of the developed models.     

Multi-generation genomic prediction of maize yield using parametric and non-parametric sparse selection indices

Genomic prediction models are often calibrated using multi-generation data. Over time, as data accumulates, training data sets become increasingly heterogeneous. Differences in allele frequency and linkage disequilibrium patterns between the training and prediction genotypes may limit prediction accuracy. This leads to the question of whether all available data or a subset of it should be used to calibrate genomic prediction models. Previous research on training set optimization has focused on identifying a subset of the available data that is optimal for a given prediction set. However, this approach does not contemplate the possibility that different training sets may be optimal for different prediction genotypes. To address this problem, we recently introduced a sparse selection index (SSI) that identifies an optimal training set for each individual in a prediction set. Using additive genomic relationships, the SSI can provide increased accuracy relative to genomic-BLUP (GBLUP). Non-parametric genomic models using Gaussian kernels (KBLUP) have, in some cases, yielded higher prediction accuracies than standard additive models. Therefore, here we studied whether combining SSIs and kernel methods could further improve prediction accuracy when training genomic models using multi-generation data. Using four years of doubled haploid maize data from the International Maize and Wheat Improvement Center (CIMMYT), we found that when predicting grain yield the KBLUP outperformed the GBLUP, and that using SSI with additive relationships (GSSI) lead to 5–17% increases in accuracy, relative to the GBLUP. However, differences in prediction accuracy between the KBLUP and the kernel-based SSI were smaller and not always significant.Subject terms: Quantitative trait, Genetic models     

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.     

Susceptible-infected-recovered epidemics in dynamic contact networks

Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the duration of an outbreak. In reality, contact patterns may be quite fluid, with individuals frequently making and breaking social or sexual relationships. Here, we develop a mathematical approach to predicting disease transmission on dynamic networks in which each individual has a characteristic behaviour (typical contact number), but the identities of their contacts change in time. We show that dynamic contact patterns shape epidemiological dynamics in ways that cannot be adequately captured in static network models or mass-action models. Our new model interpolates smoothly between static network models and mass-action models using a mixing parameter, thereby providing a bridge between disparate classes of epidemiological models. Using epidemiological and sexual contact data from an Atlanta high school, we demonstrate the application of this method for forecasting and controlling sexually transmitted disease outbreaks.     

OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany

Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations.