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As more clinical workflows continue to be augmented by artificial intelligence (AI), AI literacy among physicians will become a critical requirement for ensuring safe and ethical AI-enabled patient care. Despite the evolving importance of AI in healthcare, the extent to which it has been adopted into traditional and often-overloaded medical curricula is currently unknown. In a scoping review of 1,699 articles published between January 2016 and June 2024, we identified 18 studies which propose guiding frameworks, and 11 studies documenting real-world instruction, centered around the integration of AI into medical education. We found that comprehensive guidelines will require greater clinical relevance and personalization to suit medical student interests and career trajectories. Current efforts highlight discrepancies in the teaching guidelines, emphasizing AI evaluation and ethics over technical topics such as data science and coding. Additionally, we identified several challenges associated with integrating AI training into the medical education program, including a lack of guidelines to define medical students AI literacy, a perceived lack of proven clinical value, and a scarcity of qualified instructors. With this knowledge, we propose an AI literacy framework to define competencies for medical students. To prioritize relevant and personalized AI education, we categorize literacy into four dimensions: Foundational, Practical, Experimental, and Ethical, with tailored learning objectives to the pre-clinical, clinical, and clinical research stages of medical education. This review provides a road map for developing practical and relevant education strategies for building an AI-competent healthcare workforce., Comment: 25 pages, 2 figures, 3 tables

Given the sheer volume of surgical procedures and the significant rate of postoperative fatalities, assessing and managing surgical complications has become a critical public health concern. Existing artificial intelligence (AI) tools for risk surveillance and diagnosis often lack adequate interpretability, fairness, and reproducibility. To address this, we proposed an Explainable AI (XAI) framework designed to answer five critical questions: why, why not, how, what if, and what else, with the goal of enhancing the explainability and transparency of AI models. We incorporated various techniques such as Local Interpretable Model-agnostic Explanations (LIME), SHapley Additive exPlanations (SHAP), counterfactual explanations, model cards, an interactive feature manipulation interface, and the identification of similar patients to address these questions. We showcased an XAI interface prototype that adheres to this framework for predicting major postoperative complications. This initial implementation has provided valuable insights into the vast explanatory potential of our XAI framework and represents an initial step towards its clinical adoption., Comment: 32 pages, 7 figures, 4 supplement figures and 1 supplement table

Modern electronic health records (EHRs) hold immense promise in tracking personalized patient health trajectories through sequential deep learning, owing to their extensive breadth, scale, and temporal granularity. Nonetheless, how to effectively leverage multiple modalities from EHRs poses significant challenges, given its complex characteristics such as high dimensionality, multimodality, sparsity, varied recording frequencies, and temporal irregularities. To this end, this paper introduces a novel multimodal contrastive learning framework, specifically focusing on medical time series and clinical notes. To tackle the challenge of sparsity and irregular time intervals in medical time series, the framework integrates temporal cross-attention transformers with a dynamic embedding and tokenization scheme for learning multimodal feature representations. To harness the interconnected relationships between medical time series and clinical notes, the framework equips a global contrastive loss, aligning a patient's multimodal feature representations with the corresponding discharge summaries. Since discharge summaries uniquely pertain to individual patients and represent a holistic view of the patient's hospital stay, machine learning models are led to learn discriminative multimodal features via global contrasting. Extensive experiments with a real-world EHR dataset demonstrated that our framework outperformed state-of-the-art approaches on the exemplar task of predicting the occurrence of nine postoperative complications for more than 120,000 major inpatient surgeries using multimodal data from UF health system split among three hospitals (UF Health Gainesville, UF Health Jacksonville, and UF Health Jacksonville-North)., Comment: 12 pages, 3 figures. arXiv admin note: text overlap with arXiv:2403.04012

Background: The accurate prediction of postoperative complication risk using Electronic Health Records (EHR) and artificial intelligence shows great potential. Training a robust artificial intelligence model typically requires large-scale and diverse datasets. In reality, collecting medical data often encounters challenges surrounding privacy protection. Methods: This retrospective cohort study includes adult patients who were admitted to UFH Gainesville (GNV) (n = 79,850) and Jacksonville (JAX) (n = 28,636) for any type of inpatient surgical procedure. Using perioperative and intraoperative features, we developed federated learning models to predict nine major postoperative complications (i.e., prolonged intensive care unit stay and mechanical ventilation). We compared federated learning models with local learning models trained on a single site and central learning models trained on pooled dataset from two centers. Results: Our federated learning models achieved the area under the receiver operating characteristics curve (AUROC) values ranged from 0.81 for wound complications to 0.92 for prolonged ICU stay at UFH GNV center. At UFH JAX center, these values ranged from 0.73-0.74 for wound complications to 0.92-0.93 for hospital mortality. Federated learning models achieved comparable AUROC performance to central learning models, except for prolonged ICU stay, where the performance of federated learning models was slightly higher than central learning models at UFH GNV center, but slightly lower at UFH JAX center. In addition, our federated learning model obtained comparable performance to the best local learning model at each center, demonstrating strong generalizability. Conclusion: Federated learning is shown to be a useful tool to train robust and generalizable models from large scale data across multiple institutions where data protection barriers are high., Comment: 57 pages. 2 figures, 3 tables, 2 supplemental figures, 8 supplemental tables

The breadth, scale, and temporal granularity of modern electronic health records (EHR) systems offers great potential for estimating personalized and contextual patient health trajectories using sequential deep learning. However, learning useful representations of EHR data is challenging due to its high dimensionality, sparsity, multimodality, irregular and variable-specific recording frequency, and timestamp duplication when multiple measurements are recorded simultaneously. Although recent efforts to fuse structured EHR and unstructured clinical notes suggest the potential for more accurate prediction of clinical outcomes, less focus has been placed on EHR embedding approaches that directly address temporal EHR challenges by learning time-aware representations from multimodal patient time series. In this paper, we introduce a dynamic embedding and tokenization framework for precise representation of multimodal clinical time series that combines novel methods for encoding time and sequential position with temporal cross-attention. Our embedding and tokenization framework, when integrated into a multitask transformer classifier with sliding window attention, outperformed baseline approaches on the exemplar task of predicting the occurrence of nine postoperative complications of more than 120,000 major inpatient surgeries using multimodal data from three hospitals and two academic health centers in the United States., Comment: ICLR 2024 Workshop on Learning From Time Series for Health. 10 pages, 3 figures

During collaborative learning, confusion and conflict emerge naturally. However, persistent confusion or conflict have the potential to generate frustration and significantly impede learners' performance. Early automatic detection of confusion and conflict would allow us to support early interventions which can in turn improve students' experience with and outcomes from collaborative learning. Despite the extensive studies modeling confusion during solo learning, there is a need for further work in collaborative learning. This paper presents a multimodal machine-learning framework that automatically detects confusion and conflict during collaborative learning. We used data from 38 elementary school learners who collaborated on a series of programming tasks in classrooms. We trained deep multimodal learning models to detect confusion and conflict using features that were automatically extracted from learners' collaborative dialogues, including (1) language-derived features including TF-IDF, lexical semantics, and sentiment, (2) audio-derived features including acoustic-prosodic features, and (3) video-derived features including eye gaze, head pose, and facial expressions. Our results show that multimodal models that combine semantics, pitch, and facial expressions detected confusion and conflict with the highest accuracy, outperforming all unimodal models. We also found that prosodic cues are more predictive of conflict, and facial cues are more predictive of confusion. This study contributes to the automated modeling of collaborative learning processes and the development of real-time adaptive support to enhance learners' collaborative learning experience in classroom contexts., Comment: 27 pages, 7 figures, 7 tables

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used differential equation solver library in a high-level language (Julia's DifferentialEquations.jl) and enables GPU acceleration without requiring code changes by the user. Our approach achieves state-of-the-art performance compared to hand-optimized CUDA-C++ kernels while performing 20--100$\times$ faster than the vectorizing map (vmap) approach implemented in JAX and PyTorch. Performance evaluation on NVIDIA, AMD, Intel, and Apple GPUs demonstrates performance portability and vendor-agnosticism. We show composability with MPI to enable distributed multi-GPU workflows. The implemented solvers are fully featured -- supporting event handling, automatic differentiation, and incorporation of datasets via the GPU's texture memory -- allowing scientists to take advantage of GPU acceleration on all major current architectures without changing their model code and without loss of performance. We distribute the software as an open-source library https://github.com/SciML/DiffEqGPU.jl, Comment: 14 figures

Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using extrapolation methods which exploit "parallelism within the method" so that arbitrary user ODEs can be parallelized. We describe the specific choices made in the implementation of the explicit and implicit extrapolation methods which allow for generating low overhead static schedules to then exploit with optimized multi-threaded implementations. We demonstrate that while the multi-threading gives a noticeable acceleration on both explicit and implicit problems, the explicit parallel extrapolation methods gave no significant improvement over state-of-the-art even with a multi-threading advantage against current optimized high order Runge-Kutta tableaus. However, we demonstrate that the implicit parallel extrapolation methods are able to achieve state-of-the-art performance (2x-4x) on standard multicore x86 CPUs for systems of $<200$ stiff ODEs solved at low tolerance, a typical setup for a vast majority of users of high level language equation solver suites. The resulting method is distributed as the first widely available open source software for within-method parallel acceleration targeting typical modest compute architectures., Comment: 6 figures

Most computer algebra systems (CAS) support symbolic integration as core functionality. The majority of the integration packages use a combination of heuristic algebraic and rule-based (integration table) methods. In this paper, we present a hybrid (symbolic-numeric) methodology to calculate the indefinite integrals of univariate expressions. The primary motivation for this work is to add symbolic integration functionality to a modern CAS (the symbolic manipulation packages of SciML, the Scientific Machine Learning ecosystem of the Julia programming language), which is mainly designed toward numerical and machine learning applications and has a different set of features than traditional CAS. The symbolic part of our method is based on the combination of candidate terms generation (borrowed from the Homotopy operators theory) with rule-based expression transformations provided by the underlying CAS. The numeric part is based on sparse-regression, a component of Sparse Identification of Nonlinear Dynamics (SINDy) technique. We show that this system can solve a large variety of common integration problems using only a few dozen basic integration rules., Comment: 8 pages. submitted to ISSAC 2022. Code at https://github.com/SciML/SymbolicNumericIntegration.jl

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of NeuralPDE.jl and show how a formulation structured around numerical quadrature gives rise to new loss functions which allow for adaptivity towards bounded error tolerances. We describe the various ways one can use the tool, detailing mathematical techniques like using extended loss functions for parameter estimation and operator discovery, to help potential users adopt these PINN-based techniques into their workflow. We showcase how NeuralPDE uses a purely symbolic formulation so that all of the underlying training code is generated from an abstract formulation, and show how to make use of GPUs and solve systems of PDEs. Afterwards we give a detailed performance analysis which showcases the trade-off between training techniques on a large set of PDEs. We end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman (DFN) Model, and showcase how this PDE can be formulated and solved with NeuralPDE. Together this manuscript is meant to be a detailed and approachable technical report to help potential users of the technique quickly get a sense of the real-world performance trade-offs and use cases of the PINN techniques., Comment: 74 pages, 20+ figures, 20+ tables

In this paper we introduce JuliaSim, a high-performance programming environment designed to blend traditional modeling and simulation with machine learning. JuliaSim can build accelerated surrogates from component-based models, such as those conforming to the FMI standard, using continuous-time echo state networks (CTESN). The foundation of this environment, ModelingToolkit.jl, is an acausal modeling language which can compose the trained surrogates as components within its staged compilation process. As a complementary factor we present the JuliaSim model library, a standard library with differential-algebraic equations and pre-trained surrogates, which can be composed using the modeling system for design, optimization, and control. We demonstrate the effectiveness of the surrogate-accelerated modeling and simulation approach on HVAC dynamics by showing that the CTESN surrogates accurately capture the dynamics of a HVAC cycle at less than 4\% error while accelerating its simulation by 340x. We illustrate the use of surrogate acceleration in the design process via global optimization of simulation parameters using the embedded surrogate, yielding a speedup of two orders of magnitude to find the optimum. We showcase the surrogate deployed in a co-simulation loop, as a drop-in replacement for one of the coupled FMUs, allowing engineers to effectively explore the design space of a coupled system. Together this demonstrates a workflow for automating the integration of machine learning techniques into traditional modeling and simulation processes.

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the number of layers in a recurrent model. While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver. But, can we force the NDE to learn the version with the least steps while not increasing the training cost? Current strategies to overcome slow prediction require high order automatic differentiation, leading to significantly higher training time. We describe a novel regularization method that uses the internal cost heuristics of adaptive differential equation solvers combined with discrete adjoint sensitivities to guide the training process towards learning NDEs that are easier to solve. This approach opens up the blackbox numerical analysis behind the differential equation solver's algorithm and directly uses its local error estimates and stiffness heuristics as cheap and accurate cost estimates. We incorporate our method without any change in the underlying NDE framework and show that our method extends beyond Ordinary Differential Equations to accommodate Neural Stochastic Differential Equations. We demonstrate how our approach can halve the prediction time and, unlike other methods which can increase the training time by an order of magnitude, we demonstrate similar reduction in training times. Together this showcases how the knowledge embedded within state-of-the-art equation solvers can be used to enhance machine learning., Comment: Proceedings of the 38 th International Conference on Machine Learning, 2021

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. We demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We showcase an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODE in the classical stiff ODE systems of Robertson's problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson's problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODE. The success of learning stiff neural ODE opens up possibilities of using neural ODEs in applications with widely varying time-scales, like chemical dynamics in energy conversion, environmental engineering, and the life sciences.

Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe ModelingToolkit (MTK), a symbolic equation-based modeling system which allows for composable transformations to generate stable, efficient, and parallelized model implementations. MTK blurs the lines of traditional symbolic computing by acting directly on a user's numerical code. We show the ability to apply graph algorithms for automatically parallelizing and performing index reduction on code written for differential-algebraic equation (DAE) solvers, "fixing" the performance and stability of the model without requiring any changes to on the user's part. We demonstrate how composable model transformations can be combined with automated data-driven surrogate generation techniques, allowing machine learning methods to generate accelerated approximate models within an acausal modeling framework. These reduced models are shown to outperform the Dymola Modelica compiler on an HVAC model by 590x at 3\% error. Together, this demonstrates MTK as a system for bringing the latest research in graph transformations directly to modeling applications., Comment: 10 pages, 3 figures, 1 table

Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs. These costs can be amortized by evaluating a cheap surrogate of the full model. Here we present a general data-driven method, the continuous-time echo state network (CTESN), for generating surrogates of nonlinear ordinary differential equations with dynamics at widely separated timescales. We empirically demonstrate near-constant time performance using our CTESNs on a physically motivated scalable model of a heating system whose full execution time increases exponentially, while maintaining relative error of within 0.2 %. We also show that our model captures fast transients as well as slow dynamics effectively, while other techniques such as physics informed neural networks have difficulties trying to train and predict the highly nonlinear behavior of these models.

In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approaches. We describe a mathematical object, which we denote universal differential equations (UDEs), as the unifying framework connecting the ecosystem. We show how a wide variety of applications, from automatically discovering biological mechanisms to solving high-dimensional Hamilton-Jacobi-Bellman equations, can be phrased and efficiently handled through the UDE formalism and its tooling. We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints. This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU accelerators., Comment: 5 figures, 2 tables, 11 supplemental figures, 29 pages, 25 supplemental pages

DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations. We demonstrate the ability to incorporate DifferentialEquations.jl-defined differential equation problems into a Flux-defined neural network, and vice versa. The advantages of being able to use the entire DifferentialEquations.jl suite for this purpose is demonstrated by counter examples where simple integration strategies fail, but the sophisticated integration strategies provided by the DifferentialEquations.jl library succeed. This is followed by a demonstration of delay differential equations and stochastic differential equations inside of neural networks. We show high-level functionality for defining neural ordinary differential equations (neural networks embedded into the differential equation) and describe the extra models in the Flux model zoo which includes neural stochastic differential equations. We conclude by discussing the various adjoint methods used for backpropogation of the differential equation solvers. DiffEqFlux.jl is an important contribution to the area, as it allows the full weight of the differential equation solvers developed from decades of research in the scientific computing field to be readily applied to the challenges posed by machine learning and data science., Comment: Julialang Blog post, DiffEqFlux.jl

Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be difficult for practitioners to understand which method is likely to be the most effective on their particular application. In this manuscript we investigate the performance characteristics of Discrete Local Sensitivity Analysis implemented via Automatic Differentiation (DSAAD) against continuous adjoint sensitivity analysis. Non-stiff and stiff biological and pharmacometric models, including a PDE discretization, are used to quantify the performance of sensitivity analysis methods. Our benchmarks show that on small systems of ODEs (approximately $<100$ parameters+ODEs), forward-mode DSAAD is more efficient than both reverse-mode and continuous forward/adjoint sensitivity analysis. The scalability of continuous adjoint methods is shown to be more efficient than discrete adjoints and forward methods after crossing this size range. These comparative studies demonstrate a trade-off between memory usage and performance in the continuous adjoint methods that should be considered when choosing the technique, while numerically unstable backsolve techniques from the machine learning literature are demonstrated as unsuitable for most scientific models. The performance of adjoint methods is shown to be heavily tied to the reverse-mode AD method, with tape-based AD methods shown to be 2 orders of magnitude slower on nonlinear partial differential equations than static AD techniques. These results also demonstrate the applicability of DSAAD to differential-algebraic equations, delay differential equations, and hybrid differential equation systems, showcasing an ease of implementation advantage for DSAAD approaches., Comment: 13 pages, 3 figures, 2 tables