Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior efforts have focused mostly on identifying single equations, typically framed as symbolic regression, there remains a lack of comprehensive benchmarks for discovering dynamical models. To address this, we introduce MDBench, an open-source benchmarking framework for evaluating model discovery methods on dynamical systems. MDBench assesses 12 algorithms on 14 partial differential equations (PDEs) and 63 ordinary differential equations (ODEs) under varying levels of noise. Evaluation metrics include derivative prediction accuracy, model complexity, and equation fidelity. We also introduce seven challenging PDE systems from fluid dynamics and thermodynamics, revealing key limitations in current methods. Our findings illustrate that linear methods and genetic programming methods achieve the lowest prediction error for PDEs and ODEs, respectively. Moreover, linear models are in general more robust against noise. MDBench accelerates the advancement of model discovery methods by offering a rigorous, extensible benchmarking framework and a rich, diverse collection of dynamical system datasets, enabling systematic evaluation, comparison, and improvement of equation accuracy and robustness.

Discovering the governing equations of dynamical systems is a central problem across many scientific disciplines. As experimental data become increasingly available, automated equation discovery methods offer a promising data-driven approach to accelerate scientific discovery. Among these methods, genetic programming (GP) has been widely adopted due to its flexibility and interpretability. However, GP-based approaches often suffer from inefficient exploration of the symbolic search space, leading to slow convergence and suboptimal solutions. To address these limitations, we propose LLM-ODE, a large language model-aided model discovery framework that guides symbolic evolution using patterns extracted from elite candidate equations. By leveraging the generative prior of large language models, LLM-ODE produces more informed search trajectories while preserving the exploratory strengths of evolutionary algorithms. Empirical results on 91 dynamical systems show that LLM-ODE variants consistently outperform classical GP methods in terms of search efficiency and Pareto-front quality. Overall, our results demonstrate that LLM-ODE improves both efficiency and accuracy over traditional GP-based discovery and offers greater scalability to higher-dimensional systems compared to linear and Transformer-only model discovery methods.

The advanced learning paradigm, learning using privileged information (LUPI), leverages information in training that is not present at the time of prediction. In this study, we developed privileged logistic regression (PLR) models under the LUPI paradigm to detect acute respiratory distress syndrome (ARDS), with mechanical ventilation variables or chest x-ray image features employed in the privileged domain and electronic health records in the base domain. In model training, the objective of privileged logistic regression was designed to incorporate data from the privileged domain and encourage knowledge transfer across the privileged and base domains. An asymptotic analysis was also performed, yielding sufficient conditions under which the addition of privileged information increases the rate of convergence in the proposed model. Results for ARDS detection show that PLR models achieve better classification performances than logistic regression models trained solely on the base domain, even when privileged information is partially available. Furthermore, PLR models demonstrate performance on par with or superior to state-of-the-art models under the LUPI paradigm. As the proposed models are effective, easy to interpret, and highly explainable, they are ideal for other clinical applications where privileged information is at least partially available.

A model's interpretability is essential to many practical applications such as clinical decision support systems. In this article, a novel interpretable machine learning method is presented, which can model the relationship between input variables and responses in humanly understandable rules. The method is built by applying tropical geometry to fuzzy inference systems, wherein variable encoding functions and salient rules can be discovered by supervised learning. Experiments using synthetic datasets were conducted to demonstrate the performance and capacity of the proposed algorithm in classification and rule discovery. Furthermore, we present a pilot application in identifying heart failure patients that are eligible for advanced therapies as proof of principle. From our results on this particular application, the proposed network achieves the highest F1 score. The network is capable of learning rules that can be interpreted and used by clinical providers. In addition, existing fuzzy domain knowledge can be easily transferred into the network and facilitate model training. In our application, with the existing knowledge, the F1 score was improved by over 5%. The characteristics of the proposed network make it promising in applications requiring model reliability and justification.

Patients recovering from cardiovascular surgeries may develop life-threatening complications such as hemodynamic decompensation, making the monitoring of patients for such complications an essential component of postoperative care. However, this need has given rise to an inexorable increase in the number and modalities of data points collected, making it challenging to effectively analyze in real time. While many algorithms exist to assist in monitoring these patients, they often lack accuracy and specificity, leading to alarm fatigue among healthcare practitioners. In this study we propose a multimodal approach that incorporates salient physiological signals and EHR data to predict the onset of hemodynamic decompensation. A retrospective dataset of patients recovering from cardiac surgery was created and used to train predictive models. Advanced signal processing techniques were employed to extract complex features from physiological waveforms, while a novel tensor-based dimensionality reduction method was used to reduce the size of the feature space. These methods were evaluated for predicting the onset of decompensation at varying time intervals, ranging from a half-hour to 12 h prior to a decompensation event. The best performing models achieved AUCs of 0.87 and 0.80 for the half-hour and 12-h intervals respectively. These analyses evince that a multimodal approach can be used to develop clinical decision support systems that predict adverse events several hours in advance.

Optical colonoscopy is an essential diagnostic and prognostic tool for many gastrointestinal diseases, including cancer screening and staging, intestinal bleeding, diarrhea, abdominal symptom evaluation, and inflammatory bowel disease assessment. However, the evaluation, classification, and quantification of findings from colonoscopy are subject to inter-observer variation. Automated assessment of colonoscopy is of interest considering the subjectivity present in qualitative human interpretations of colonoscopy findings. Localization of the camera is essential to interpreting the meaning and context of findings for diseases evaluated by colonoscopy. In this study, we propose a camera localization system to estimate the relative location of the camera and classify the colon into anatomical segments. The camera localization system begins with non-informative frame detection and removal. Then a self-training end-to-end convolutional neural network is built to estimate the camera motion, where several strategies are proposed to improve its robustness and generalization on endoscopic videos. Using the estimated camera motion a camera trajectory can be derived and a relative location index calculated. Based on the estimated location index, anatomical colon segment classification is performed by constructing a colon template. The proposed motion estimation algorithm was evaluated on an external dataset containing the ground truth for camera pose. The experimental results show that the performance of the proposed method is superior to other published methods. The relative location index estimation and anatomical region classification were further validated using colonoscopy videos collected from routine clinical practice. This validation yielded an average accuracy in classification of 0.754, which is substantially higher than the performances obtained using location indices built from other methods.

Acute respiratory distress syndrome (ARDS) is a fulminant inflammatory lung injury that develops in patients with critical illnesses, affecting 200,000 patients in the United States annually. However, a recent study suggests that most patients with ARDS are diagnosed late or missed completely and fail to receive life-saving treatments. This is primarily due to the dependency of current diagnosis criteria on chest x-ray, which is not necessarily available at the time of diagnosis. In machine learning, such an information is known as Privileged Information - information that is available at training but not at testing. However, in diagnosing ARDS, privileged information (chest x-rays) are sometimes only available for a portion of the training data. To address this issue, the Learning Using Partially Available Privileged Information (LUPAPI) paradigm is proposed. As there are multiple ways to incorporate partially available privileged information, three models built on classical SVM are described. Another complexity of diagnosing ARDS is the uncertainty in clinical interpretation of chest x-rays. To address this, the LUPAPI framework is then extended to incorporate label uncertainty, resulting in a novel and comprehensive machine learning paradigm - Learning Using Label Uncertainty and Partially Available Privileged Information (LULUPAPI). The proposed frameworks use Electronic Health Record (EHR) data as regular information, chest x-rays as partially available privileged information, and clinicians' confidence levels in ARDS diagnosis as a measure of label uncertainty. Experiments on an ARDS dataset demonstrate that both the LUPAPI and LULUPAPI models outperform SVM, with LULUPAPI performing better than LUPAPI.

Traumatic brain injury (TBI) is a major cause of death and disability worldwide. Automated brain hematoma segmentation and outcome prediction for patients with TBI can effectively facilitate patient management. In this study, we propose a novel Multi-view convolutional neural network with a mixed loss to segment total acute hematoma on head CT scans collected within 24 h after the injury. Based on the automated segmentation, the volumetric distribution and shape characteristics of the hematoma were extracted and combined with other clinical observations to predict 6-month mortality. The proposed hematoma segmentation network achieved an average Dice coefficient of 0.697 and an intraclass correlation coefficient of 0.966 between the volumes estimated from the predicted hematoma segmentation and volumes of the annotated hematoma segmentation on the test set. Compared with other published methods, the proposed method has the most accurate segmentation performance and volume estimation. For 6-month mortality prediction, the model achieved an average area under the precision-recall curve (AUCPR) of 0.559 and area under the receiver operating characteristic curve (AUC) of 0.853 using 10-fold cross-validation on a dataset consisting of 828 patients. The average AUCPR and AUC of the proposed model are respectively more than 10% and 5% higher than those of the widely used IMPACT model.

Traumatic brain injury (TBI) is a major health and socioeconomic problem globally that is associated with a high level of mortality. Early and accurate diagnosis and prognosis of TBI is important in patient management and preventing any secondary injuries. Computer tomography (CT) imaging assists physicians in diagnosing injury and guiding treatment. One of the clinical parameters extracted from CT images is midline shift, a measure of linear displacement in brain structure, which is correlated with TBI patient outcomes. However, only a tiny fraction of the overall tissue displacement is quantified through this parameter. In this paper, a novel measurement of overall mid-surface shift is proposed that quantifies the total volume of brain tissue shifted across the midline. When compared to traditional midline shift, mid-surface shift has a stronger correlation with TBI patient outcomes.

Determining the appropriate timing of mechanical circulatory support (MCS) or heart transplantation (HT) for patients with advanced heart failure is essential as there may be a mortality cost to delayed care. An automated decision-making system that can identify patients eligible for a HT/MCS would facilitate primary care physicians or general cardiologists referring those patients for consideration of advanced therapies. In this study, a novel fuzzy neural network was built by integrating fuzzy set theory, neural network, and genetic algorithm techniques. The overall architecture of the proposed fuzzy neural network was inspired by clinical practice guidelines. Clinical variables were encoded using fuzzy concepts and rules were calculated in a fully-connected layer with constraints in weights. From the experiments, the proposed fuzzy neural network achieved an average AUC of 0.838 and an F1 score of 0.462. The rules from the trained network were further analyzed. Our results show that the proposed fuzzy neural network can not only achieve good classification performance, but also provides transparency with respect to knowledge extraction and interpretation.