Generative AI unlocks PET insights: brain amyloid dynamics and quantification.

Introduction: Studying the spatiotemporal patterns of amyloid accumulation in the brain over time is crucial in understanding Alzheimer's disease (AD). Positron Emission Tomography (PET) imaging plays a pivotal role because it allows for the visualization and quantification of abnormal amyloid beta (Aß) load in the living brain, providing a powerful tool for tracking disease progression and evaluating the efficacy of anti-amyloid therapies. Generative artificial intelligence (AI) can learn complex data distributions and generate realistic synthetic images. In this study, we demonstrate for the first time the potential of Generative Adversarial Networks (GANs) to build a low-dimensional representation space that effectively describes brain amyloid load and its dynamics. Methods: Using a cohort of 1,259 subjects with AV45 PET images from the Alzheimer's Disease Neuroimaging Initiative (ADNI), we develop a 3D GAN model to project images into a latent representation space and generate back synthetic images. Then, we build a progression model on the representation space based on non-parametric ordinary differential equations to study brain amyloid evolution. Results: We found that global SUVR can be accurately predicted with a linear regression model only from the latent representation space (RMSE = 0.08 ± 0.01). We generated synthetic PET trajectories and illustrated predicted Aß change in four years compared with actual progression. Discussion: Generative AI can generate rich representations for statistical prediction and progression modeling and simulate evolution in synthetic patients, providing an invaluable tool for understanding AD, assisting in diagnosis, and designing clinical trials. The aim of this study was to illustrate the huge potential that generative AI has in brain amyloid imaging and to encourage its advancement by providing use cases and ideas for future research tracks.

Mathematical Modeling Suggests That Monocyte Activity May Drive Sex Disparities during Influenza Infection.

In humans, females of reproductive age often experience a more severe disease during influenza A virus infection, which may be due to differences in their innate immune response. Sex-specific outcomes to influenza infection have been recapitulated in mice, enabling researchers to study viral and immune dynamics in vivo in order to identify immune mechanisms that are differently regulated between the sexes. This study is based on the hypothesis that sex-specific outcomes emerge due to differences in the rates/speeds that select immune components respond. Using publicly available sex-specific murine data, we utilized dynamic mathematical models of the innate immune response to identify candidate mechanisms that may lead to increased disease severity in female mice. We implemented a large computational screen using the Bayesian information criterion (BIC), wherein the goodness of fit of the competing model scenarios is balanced against complexity (i.e., the number of parameters). Our results suggest that having sex-specific rates for proinflammatory monocyte induction by interferon and monocyte inhibition of virus replication provides the simplest (lowest BIC) explanation for the difference observed in the male and female immune responses. Markov-chain Monte Carlo (MCMC) analysis and global sensitivity analysis of the top performing scenario were performed to provide rigorous estimates of the sex-specific parameter distributions and to provide insight into which parameters most affect innate immune responses. Simulations using the top-performing model suggest that monocyte activity could be a key target to reduce influenza disease severity in females. Overall, our Bayesian statistical and dynamic modeling approach suggests that monocyte activity and induction parameters are sex-specific and may explain sex-differences in influenza disease immune dynamics.

A mechanistic modelling approach of the host-microbiota interactions to investigate beneficial symbiotic resilience in the human gut.

The health and well-being of a host are deeply influenced by the interactions with its gut microbiota. Contrasted environmental conditions, such as diseases or dietary habits, play a pivotal role in modulating these interactions, impacting microbiota composition and functionality. Such conditions can also lead to transitions from beneficial to detrimental symbiosis, viewed as alternative stable states of the host-microbiota dialogue. This article introduces a novel mathematical model exploring host-microbiota interactions, integrating dynamics of the colonic epithelial crypt, microbial metabolic functions, inflammation sensitivity and colon flows in a transverse section. The model considers metabolic shifts in epithelial cells based on butyrate and hydrogen sulfide concentrations, innate immune pattern recognition receptor activation, microbial oxygen tolerance and the impact of antimicrobial peptides on the microbiota. Using the model, we demonstrated that a high-protein, low-fibre diet exacerbates detrimental interactions and compromises beneficial symbiotic resilience, underscoring a destabilizing effect towards an unhealthy state. Moreover, the proposed model provides essential insights into oxygen levels, fibre and protein breakdown, and basic mechanisms of innate immunity in the colon and offers a crucial understanding of factors influencing the colon environment.

Merits and Demerits of Machine Learning of Ferroelectric, Flexoelectric, and Electrolytic Properties of Ceramic Materials.

In the present review, the merits and demerits of machine learning (ML) in materials science are discussed, compared with first principles calculations (PDE (partial differential equations) model) and physical or phenomenological ODE (ordinary differential equations) model calculations. ML is basically a fitting procedure of pre-existing (experimental) data as a function of various factors called descriptors. If excellent descriptors can be selected and the training data contain negligible error, the predictive power of a ML model is relatively high. However, it is currently very difficult for a ML model to predict experimental results beyond the parameter space of the training experimental data. For example, it is pointed out that all-dislocation-ceramics, which could be a new type of solid electrolyte filled with appropriate dislocations for high ionic conductivity without dendrite formation, could not be predicted by ML. The merits and demerits of first principles calculations and physical or phenomenological ODE model calculations are also discussed with some examples of the flexoelectric effect, dielectric constant, and ionic conductivity in solid electrolytes.

Mathematical modeling and analysis of cancer treatment with radiation and anti-PD-L1.

In cancer treatment, radiation therapy (RT) induces direct tumor cell death due to DNA damage, but it also enhances the deaths of radiosensitive immune cells and is followed by local relapse and up-regulation of immune checkpoint ligand PD-L1. Since the binding between PD-1 and PD-L1 curtails anti-tumor immunities, combining RT and PD-L1 inhibitor, anti-PD-L1, is a potential method to improve the treatment efficacy by RT. Some experiments support this hypothesis by showing that the combination of ionizing irradiation (IR) and anti-PD-L1 improves tumor reduction comparing to the monotherapy of IR or anti-PD-L1. In this work, we create a simplified ODE model to study the order of tumor growths under treatments of IR and anti-PD-L1. Our synergy analysis indicates that both IR and anti-PD-L1 improve the tumor reduction of each other, when IR and anti-PD-L1 are given simultaneously. When giving IR and anti-PD-L1 separately, a high dosage of IR should be given first to efficiently reduce tumor load and then followed by anti-PD-L1 with strong efficacy to maintain the tumor reduction and slow down the relapse. Increasing the duration of anti-PD-L1 improves the tumor reduction, but it cannot prolong the duration that tumor relapses to the level of the control case. Under some simplification, we also prove that the model has an unstable tumor free equilibrium and a locally asymptotically stable tumor persistent equilibrium. Our bifurcation diagram reveals a transition from tumor elimination to tumor persistence, as the tumor growth rate increases. In the tumor persistent case, both anti-PD-L1 and IR can reduce tumor amount in the long term.

Classification of 2-node excitatory-inhibitory networks.

We classify connected 2-node excitatory-inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different types of excitatory-inhibitory networks: restricted, partially restricted, unrestricted and completely unrestricted. For each type we give two different classifications. Using results on ODE-equivalence and minimality, we classify the ODE-classes and present a minimal representative for each ODE-class. We also classify all the networks with valence ≤2. These classifications are up to renumbering of nodes and the interchange of 'excitatory' and 'inhibitory' on nodes and arrows. These classifications constitute a first step towards analysing dynamics and bifurcations of excitatory-inhibitory networks. The results have potential applications to biological network models, especially neuronal networks, gene regulatory networks, and synthetic gene networks.

Biobased short chain fatty acid production - Exploring microbial community dynamics and metabolic networks through kinetic and microbial modeling approaches.

In recent years, there has been growing interest in harnessing anaerobic digestion technology for resource recovery from waste streams. This approach has evolved beyond its traditional role in energy generation to encompass the production of valuable carboxylic acids, especially volatile fatty acids (VFAs) like acetic acid, propionic acid, and butyric acid. VFAs hold great potential for various industries and biobased applications due to their versatile properties. Despite increasing global demand, over 90% of VFAs are currently produced synthetically from petrochemicals. Realizing the potential of large-scale biobased VFA production from waste streams offers significant eco-friendly opportunities but comes with several key challenges. These include low VFA production yields, unstable acid compositions, complex and expensive purification methods, and post-processing needs. Among these, production yield and acid composition stand out as the most critical obstacles impacting economic viability and competitiveness. This paper seeks to offer a comprehensive view of combining complementary modeling approaches, including kinetic and microbial modeling, to understand the workings of microbial communities and metabolic pathways in VFA production, enhance production efficiency, and regulate acid profiles through the integration of omics and bioreactor data.

Unraveling IFN-I response dynamics and TNF crosstalk in the pathophysiology of systemic lupus erythematosus.

Introduction: The innate immune system serves the crucial first line of defense against a wide variety of potential threats, during which the production of pro-inflammatory cytokines IFN-I and TNFα are key. This astonishing power to fight invaders, however, comes at the cost of risking IFN-I-related pathologies, such as observed during autoimmune diseases, during which IFN-I and TNFα response dynamics are dysregulated. Therefore, these response dynamics must be tightly regulated, and precisely matched with the potential threat. This regulation is currently far from understood. Methods: Using droplet-based microfluidics and ODE modeling, we studied the fundamentals of single-cell decision-making upon TLR signaling in human primary immune cells (n = 23). Next, using biologicals used for treating autoimmune diseases [i.e., anti-TNFα, and JAK inhibitors], we unraveled the crosstalk between IFN-I and TNFα signaling dynamics. Finally, we studied primary immune cells isolated from SLE patients (n = 8) to provide insights into SLE pathophysiology. Results: single-cell IFN-I and TNFα response dynamics display remarkable differences, yet both being highly heterogeneous. Blocking TNFα signaling increases the percentage of IFN-I-producing cells, while blocking IFN-I signaling decreases the percentage of TNFα-producing cells. Single-cell decision-making in SLE patients is dysregulated, pointing towards a dysregulated crosstalk between IFN-I and TNFα response dynamics. Discussion: We provide a solid droplet-based microfluidic platform to study inherent immune secretory behaviors, substantiated by ODE modeling, which can challenge the conceptualization within and between different immune signaling systems. These insights will build towards an improved fundamental understanding on single-cell decision-making in health and disease.

On inductive biases for the robust and interpretable prediction of drug concentrations using deep compartment models.

Conventional pharmacokinetic (PK) models contain several useful inductive biases guiding model convergence to more realistic predictions of drug concentrations. Implementing similar biases in standard neural networks can be challenging, but might be fundamental for model robustness and predictive performance. In this study, we build on the deep compartment model (DCM) architecture by introducing constraints that guide the model to explore more physiologically realistic solutions. Using a simulation study, we show that constraints improve robustness in sparse data settings. Additionally, predicted concentration-time curves took on more realistic shapes compared to unconstrained models. Next, we propose the use of multi-branch networks, where each covariate can be connected to specific PK parameters, to reduce the propensity of models to learn spurious effects. Another benefit of this architecture is that covariate effects are isolated, enabling model interpretability through the visualization of learned functions. We show that all models were sensitive to learning false effects when trained in the presence of unimportant covariates, indicating the importance of selecting an appropriate set of covariates to link to the PK parameters. Finally, we compared the predictive performance of the constrained models to previous relevant population PK models on a real-world data set of 69 haemophilia A patients. Here, constrained models obtained higher accuracy compared to the standard DCM, with the multi-branch network outperforming previous PK models. We conclude that physiological-based constraints can improve model robustness. We describe an interpretable architecture which aids model trust, which will be key for the adoption of machine learning-based models in clinical practice.

Modeling county level COVID-19 transmission in the greater St. Louis area: Challenges of uncertainty and identifiability when fitting mechanistic models to time-varying processes.

We use a compartmental model with a time-varying transmission parameter to describe county level COVID-19 transmission in the greater St. Louis area of Missouri and investigate the challenges in fitting such a model to time-varying processes. We fit this model to synthetic and real confirmed case and hospital discharge data from May to December 2020 and calculate uncertainties in the resulting parameter estimates. We also explore non-identifiability within the estimated parameter set. We find that the death rate of infectious non-hospitalized individuals, the testing parameter and the initial number of exposed individuals are not identifiable based on an investigation of correlation coefficients between pairs of parameter estimates. We also explore how this non-identifiability ties back into uncertainties in the estimated parameters and find that it inflates uncertainty in the estimates of our time-varying transmission parameter. However, we do find that R0 is not highly affected by non-identifiability of its constituent components and the uncertainties associated with the quantity are smaller than those of the estimated parameters. Parameter values estimated from data will always be associated with some uncertainty and our work highlights the importance of conducting these analyses when fitting such models to real data. Exploring identifiability and uncertainty is crucial in revealing how much we can trust the parameter estimates.

A review of mechanistic learning in mathematical oncology.

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

Mathematical complexities in radionuclide metabolic modelling: a review of ordinary differential equation kinetics solvers in biokinetic modelling.

Biokinetic models have been employed in internal dosimetry (ID) to model the human body's time-dependent retention and excretion of radionuclides. Consequently, biokinetic models have become instrumental in modelling the body burden from biological processes from internalized radionuclides for prospective and retrospective dose assessment. Solutions to biokinetic equations have been modelled as a system of coupled ordinary differential equations (ODEs) representing the time-dependent distribution of materials deposited within the body. In parallel, several mathematical algorithms were developed for solving general kinetic problems, upon which biokinetic solution tools were constructed. This paper provides a comprehensive review of mathematical solving methods adopted by some known internal dose computer codes for modelling the distribution and dosimetry for internal emitters, highlighting the mathematical frameworks, capabilities, and limitations. Further discussion details the mathematical underpinnings of biokinetic solutions in a unique approach paralleling advancements in ID. The capabilities of available mathematical solvers in computational systems were also emphasized. A survey of ODE forms, methods, and solvers was conducted to highlight capabilities for advancing the utilization of modern toolkits in ID. This review is the first of its kind in framing the development of biokinetic solving methods as the juxtaposition of mathematical solving schemes and computational capabilities, highlighting the evolution in biokinetic solving for radiation dose assessment.

Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial.

Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, we present a comprehensive, easy-to-use, and flexible MATLAB toolbox, QuantDiffForecast, and associated tutorial to estimate parameters and generate short-term forecasts with quantified uncertainty from dynamical models based on systems of ODEs. We provide software ( https://github.com/gchowell/paramEstimation_forecasting_ODEmodels/) and detailed guidance on estimating parameters and forecasting time-series trajectories that are characterized using ODEs with quantified uncertainty through a parametric bootstrapping approach. It includes functions that allow the user to infer model parameters and assess forecasting performance for different ODE models specified by the user, using different estimation methods and error structures in the data. The tutorial is intended for a diverse audience, including students training in dynamic systems, and will be broadly applicable to estimate parameters and generate forecasts from models based on ODEs. The functions included in the toolbox are illustrated using epidemic models with varying levels of complexity applied to data from the 1918 influenza pandemic in San Francisco. A tutorial video that demonstrates the functionality of the toolbox is included.

Periodic insulin stimulation of Akt: Dynamic steady states and robustness.

The periodic secretion of insulin is a salient feature of the blood glucose control system in vivo. Insulin levels in the blood exhibit oscillations on multiple time scales - rapid, ultradian, and circadian - and the improved metabolic regulation resulting from pulsatile insulin release has been well established. Although numerous mathematical models investigating the causal mechanisms of insulin oscillations have appeared in the literature, to date there has been comparatively little attention given to the influence of periodic insulin stimulation on downstream components of the insulin signalling pathway. In this paper, we explore the effect of high frequency periodic insulin stimulation on Akt (also known as PKB), a crucial crosstalk node in the insulin signalling pathway that coordinates metabolic and mitogenic processes in the cell. We analyse a mathematical model of Akt translocation to the plasma membrane under both single step insulin perturbations and periodic insulin stimulation with an emphasis on - but not limited to - the physiological range of parameter values. It was shown that the system rapidly attains a robust dynamic steady state entrained to the periodic insulin stimulation. Moreover, the translocation of Akt to the plasma membrane in the model permits a sufficient level of phosphorylation to trigger downstream metabolic regulators. However, the modelling also indicated that further investigation of this activation process is required to determine whether the response of Akt is a key determinant of the enhanced metabolic control observed under periodic insulin stimulation.

Bridging the gap - estimation of 2022/2023 SARS-CoV-2 healthcare burden in Germany based on multidimensional data from a rapid epidemic panel.

OBJECTIVES: Throughout the SARS-CoV-2 pandemic, Germany like other countries lacked adaptive population-based panels to monitor the spread of epidemic diseases. METHODS: To fill a gap in population-based estimates needed for winter 2022/23 we resampled in the German SARS-CoV-2 cohort study MuSPAD in mid-2022, including characterization of systemic cellular and humoral immune responses by interferon-γ-release assay (IGRA) and CLIA/IVN assay. We were able to confirm categorization of our study population into four groups with differing protection levels against severe COVID-19 courses based on literature synthesis. Using these estimates, we assessed potential healthcare burden for winter 2022/23 in different scenarios with varying assumptions on transmissibility, pathogenicity, new variants, and vaccine booster campaigns in ordinary differential equation models. RESULTS: We included 9921 participants from eight German regions. While 85% of individuals were located in one of the two highest protection categories, hospitalization estimates from scenario modeling were highly dependent on viral variant characteristics ranging from 30-300% compared to the 02/2021 peak. Our results were openly communicated and published to an epidemic panel network and a newly established modeling network. CONCLUSIONS: We demonstrate feasibility of a rapid epidemic panel to provide complex immune protection levels for inclusion in dynamic disease burden modeling scenarios.

Travelling waves due to negative plant-soil feedbacks in a model including tree life-stages.

The emergence and maintenance of tree species diversity in tropical forests is commonly attributed to the Janzen-Connell (JC) hypothesis, which states that growth of seedlings is suppressed in the proximity of conspecific adult trees. As a result, a JC distribution due to a density-dependent negative feedback emerges in the form of a (transient) pattern where conspecific seedling density is highest at intermediate distances away from parent trees. Several studies suggest that the required density-dependent feedbacks behind this pattern could result from interactions between trees and soil-borne pathogens. However, negative plant-soil feedback may involve additional mechanisms, including the accumulation of autotoxic compounds generated through tree litter decomposition. An essential task therefore consists in constructing mathematical models incorporating both effects showing the ability to support the emergence of JC distributions. In this work, we develop and analyse a novel reaction-diffusion-ODE model, describing the interactions within tropical tree species across different life stages (seeds, seedlings, and adults) as driven by negative plant-soil feedback. In particular, we show that under strong negative plant-soil feedback travelling wave solutions exist, creating transient distributions of adult trees and seedlings that are in agreement with the Janzen-Connell hypothesis. Moreover, we show that these travelling wave solutions are pulled fronts and a robust feature as they occur over a broad parameter range. Finally, we calculate their linear spreading speed and show its (in)dependence on relevant nondimensional parameters.

The effect of governance structures on optimal control of two-patch epidemic models.

Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the "governance structure") can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.

Fitting parameters and therapies of ODE tumor models with senescence and immune system.

This work is devoted to introduce and study two quasispecies nonlinear ODE systems that model the behavior of tumor cell populations organized in different states. In the first model, replicative, senescent, extended lifespan, immortal and tumor cells are considered, while the second also includes immune cells. We fit the parameters regulating the transmission between states in order to approximate the outcomes of the models to a real progressive tumor invasion. After that, we study the identifiability of the fitted parameters, by using two sensitivity analysis methods. Then, we show that an adequate reduced fitting process (only accounting to the most identifiable parameters) gives similar results but saving computational cost. Three different therapies are introduced in the models to shrink (progressively in time) the tumor, while the replicative and senescent cells invade. Each therapy is identified to a dimensionless parameter. Then, we make a fitting process of the therapies' parameters, in various scenarios depending on the initial tumor according to the time when the therapies started. We conclude that, although the optimal combination of therapies depends on the size of initial tumor, the most efficient therapy is the reinforcement of the immune system. Finally, an identifiability analysis allows us to detect a limitation in the therapy outcomes. In fact, perturbing the optimal combination of therapies under an appropriate therapeutic vector produces virtually the same results.

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling.

In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled60Co (Type M) and131I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method (expm). The differences generally observed between the implicit solvers andexpmare attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

Inferring single-cell transcriptomic dynamics with structured latent gene expression dynamics.

Gene expression dynamics provide directional information for trajectory inference from single-cell RNA sequencing data. Traditional approaches compute RNA velocity using strict modeling assumptions about transcription and splicing of RNA. This can fail in scenarios where multiple lineages have distinct gene dynamics or where rates of transcription and splicing are time dependent. We present "LatentVelo," an approach to compute a low-dimensional representation of gene dynamics with deep learning. LatentVelo embeds cells into a latent space with a variational autoencoder and models differentiation dynamics on this "dynamics-based" latent space with neural ordinary differential equations. LatentVelo infers a latent regulatory state that controls the dynamics of an individual cell to model multiple lineages. LatentVelo can predict latent trajectories, describing the inferred developmental path for individual cells rather than just local RNA velocity vectors. The dynamics-based embedding batch corrects cell states and velocities, outperforming comparable autoencoder batch correction methods that do not consider gene expression dynamics.