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When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model is accurate. Possible sources include irreducible aleatoric uncertainty due to noise in the data, epistemic uncertainty induced by insufficient data or inadequate parameterization, and model-form uncertainty related to the use of misspecified model equations. Physics-based regularization interacts in nontrivial ways with aleatoric, epistemic and model-form uncertainty and their combination, and a better understanding of this interaction is needed to improve the predictive performance of physics-informed digital twins that operate under real conditions. With a specific focus on biological and physiological models, this study investigates the decomposition of total uncertainty in the estimation of states and parameters of a differential system simulated with MC X-TFC, a new physics-informed approach for uncertainty quantification based on random projections and Monte-Carlo sampling. MC X-TFC is applied to a six-compartment stiff ODE system, the CVSim-6 model, developed in the context of human physiology. The system is analyzed by progressively removing data while estimating an increasing number of parameters and by investigating total uncertainty under model-form misspecification of non-linear resistance in the pulmonary compartment. In particular, we focus on the interaction between the formulation of the discrepancy term and quantification of model-form uncertainty, and show how additional physics can help in the estimation process. The method demonstrates robustness and efficiency in estimating unknown states and parameters, even with limited, sparse, and noisy data. It also offers great flexibility in integrating data with physics for improved estimation, even in cases of model misspecification.

The study of small ($<$300 m) near-Earth objects (NEOs) is important because they are more closely related than larger objects to the precursors of meteorites that fall on Earth. Collisions of these bodies with Earth are also more frequent. Although such collisions cannot produce massive extinction events, they can still produce significant local damage. Here we present the results of a photometric and spectroscopic survey of small NEOs, which include near-infrared (NIR) spectra of 84 objects with a mean diameter of 126 m and photometric data of 59 objects with a mean diameter of 87 m. We found that S-complex asteroids are the most abundant among the NEOs, comprising $\sim$66\% of the sample. Most asteroids in the S-complex were found to have compositions consistent with LL-chondrites. Our study revealed the existence of NEOs with spectral characteristics similar to those in the S-complex, but that could be hidden within the C- or X-complex due to their weak absorption bands. We suggest that the presence of metal or shock-darkening could be responsible for the attenuation of the absorption bands. These objects have been grouped into a new subclass within the S-complex called Sx-types. The dynamical modeling showed that 83\% of the NEOs escaped from the $\nu_{6}$ resonance, 16\% from the 3:1 and just 1\% from the 5:2 resonance. Lightcurves and rotational periods were derived from the photometric data. No clear trend between the axis ratio and the absolute magnitude or rotational period of the NEOs was found., Comment: 61 pages, 43 figures, 5 tables. Accepted for publication in the Planetary Science Journal

Carbonaceous chondrites are among the most important meteorite types and have played a vital role in deciphering the origin and evolution of our solar system. They have been linked to low-albedo C-type asteroids, but due to subdued absorption bands, definitive asteroid-meteorite linkages remain elusive. A majority of these existing linkages rely on fine-grained (typically < 45 micron) powders across a limited wavelength range in the visible to near-infrared (0.35-2.5 microns). While this is useful in interpreting the fine-grained regolith of larger main-belt objects like Ceres, recent spacecraft missions to smaller near-Earth asteroids (NEAs), such as Bennu and Ryugu, have shown that their surfaces are dominated by larger grain size material. To better interpret the surfaces of these smaller, carbonaceous NEAs, we obtained laboratory reflectance spectra of seven carbonaceous chondrite meteorite groups (CI, CM, CO, CV, CR, CK, C2-ungrouped) over the ultraviolet to mid-infrared range (0.2-14 microns). Each meteorite contained five grain size bins (45-1000 microns) to help constrain spectral grain size effects. We find a correlation between grain size and absolute reflectance, spectral slope, band depth, and the Christiansen feature band center. Principal component analysis of grain size variation illustrates a similar trend to lunar-style space weathering. We also show that the Bus-DeMeo asteroid taxonomic classification of our samples is affected by grain size, specifically shifting CM2 Aguas Zarcas from a Ch-type to B-type with increasing grain size. This has implications for the parent body of the OSIRIS-REx target, Bennu. With Aguas Zarcas, we present results from Hapke modeling., Comment: 40 pages, 15 figures, published in the Planetary Science Journal

This paper explores the impact of biologically plausible neuron models on the performance of Spiking Neural Networks (SNNs) for regression tasks. While SNNs are widely recognized for classification tasks, their application to Scientific Machine Learning and regression remains underexplored. We focus on the membrane component of SNNs, comparing four neuron models: Leaky Integrate-and-Fire, FitzHugh-Nagumo, Izhikevich, and Hodgkin-Huxley. We investigate their effect on SNN accuracy and efficiency for function regression tasks, by using Euler and Runge-Kutta 4th-order approximation schemes. We show how more biologically plausible neuron models improve the accuracy of SNNs while reducing the number of spikes in the system. The latter represents an energetic gain on actual neuromorphic chips since it directly reflects the amount of energy required for the computations.

Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is even greater when the physics underlying such systems is not yet understood, and scientific inquiry must solely rely on empirical data. Driven by the need to fill this gap, we develop a framework that learns mathematical expressions modeling complex dynamical behaviors by identifying differential equations from noisy and sparse observable data. We train a small neural network to learn the dynamics of a system, its rate of change in time, and missing model terms, which are used as input for a symbolic regression algorithm to autonomously distill the explicit mathematical terms. This, in turn, enables us to predict the future evolution of the dynamical behavior. The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems such as the well-known Lorenz system, a six-dimensional hyperchaotic system, and the non-autonomous Sprott chaotic system, and comparing them with their known analytical expressions., Comment: 28 pages, 15 figures, 9 tables

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model, and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. While the current work focuses on the performance of AI-Aristotle based on synthetic data, it can equally handle noisy experimental data and can even be used for black-box identification in just a few minutes on a laptop. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

In this work we apply a novel, accurate, fast, and robust physics-informed neural network framework for data-driven parameters discovery of problems modeled via parametric ordinary differential equations (ODEs) called the Extreme Theory of Functional Connections (X-TFC). The proposed method merges two recently developed frameworks for solving problems involving parametric DEs, 1) the Theory of Functional Connections (TFC) and 2) the Physics-Informed Neural Networks (PINN). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters governing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIR). The results show the low computational times, the high accuracy and effectiveness of the X-TFC method in performing data-driven parameters discovery of systems modeled via parametric ODEs using unperturbed and perturbed data.

In this work we present a novel, accurate, and robust physics-informed method for solving problems involving parametric differential equations (DEs) called the Extreme Theory of Functional Connections, or X-TFC. The proposed method is a synergy of two recently developed frameworks for solving problems involving parametric DEs, 1) the Theory of Functional Connections, TFC, and the Physics-Informed Neural Networks, PINN. Although this paper focuses on the solution of exact problems involving parametric DEs (i.e. problems where the modeling error is negligible) with known parameters, X-TFC can also be used for data-driven solutions and data-driven discovery of parametric DEs. In the proposed method, the latent solution of the parametric DEs is approximated by a TFC constrained expression that uses a Neural Network (NN) as the free-function. This approximate solution form always analytically satisfies the constraints of the DE, while maintaining a NN with unconstrained parameters, like the Deep-TFC method. X-TFC differs from PINN and Deep-TFC; whereas PINN and Deep-TFC use a deep-NN, X-TFC uses a single-layer NN, or more precisely, an Extreme Learning Machine, ELM. This choice is based on the properties of the ELM algorithm. In order to numerically validate the method, it was tested over a range of problems including the approximation of solutions to linear and non-linear ordinary DEs (ODEs), systems of ODEs (SODEs), and partial DEs (PDEs). Furthermore, a few of these problems are of interest in physics and engineering such as the Classic Emden-Fowler equation, the Radiative Transfer (RT) equation, and the Heat-Transfer (HT) equation. The results show that X-TFC achieves high accuracy with low computational time and thus it is comparable with the other state-of-the-art methods., Comment: 28 pages, 12 figures, 6 tables