This paper presents innovative designs for 3D-printed tumbling microrobots, specifically engineered for targeted in vivo drug delivery applications. The microrobot designs, created using stereolithography 3D printing technologies, incorporate permanent micro-magnets to enable actuation via a rotating magnetic field actuator system. The experimental framework encompasses a series of locomotion characterization tests to evaluate microrobot performance under various conditions. Testing variables include variations in microrobot geometries, actuation frequencies, and environmental conditions, such as dry and wet environments, and temperature changes. The paper outlines designs for three drug loading methods, along with comprehensive assessments thermal drug release using a focused ultrasound system, as well as biocompatibility tests. Animal model testing involves tissue phantoms and in vivo rat models, ensuring a thorough evaluation of the microrobots' performance and compatibility. The results highlight the robustness and adaptability of the proposed microrobot designs, showcasing the potential for efficient and targeted in vivo drug delivery. This novel approach addresses current limitations in existing tumbling microrobot designs and paves the way for advancements in targeted drug delivery within the large intestine.

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference -- a methodology within scientific machine learning that enables learning from data a low-dimensional representation of a high-dimensional system governed by nonlinear partial differential equations -- by embedding such state constraints in the reduced-order model predictions. In the model learning process, we propose a new way to choose regularization hyperparameters based on a key performance indicator. Since embedding state constraints improves the stability of the Operator Inference reduced-order model, we compare the proposed state constraints-embedded Operator Inference with the standard Operator Inference and other stability-enhancing approaches. For an application to char combustion, we demonstrate that the proposed approach yields state predictions superior to the other methods regarding stability and accuracy. It extrapolates over 200\% past the training regime while being computationally efficient and physically consistent.

Multi-modal large language models (MLLMs) have demonstrated promising capabilities across various tasks by integrating textual and visual information to achieve visual understanding in complex scenarios. Despite the availability of several benchmarks aims to evaluating MLLMs in tasks from visual question answering to complex problem-solving, most focus predominantly on mathematics or general visual understanding tasks. This reveals a critical gap in current benchmarks, which often overlook the inclusion of other key scientific disciplines such as physics and chemistry. To address this gap, we meticulously construct a comprehensive benchmark, named VisScience, which is utilized to assess the multi-modal scientific reasoning across the three disciplines of mathematics, physics, and chemistry. This benchmark comprises 3,000 questions drawn from K12 education - spanning elementary school through high school - equally distributed across three disciplines, with 1,000 questions per discipline. The questions within VisScience span 21 distinct subjects and are categorized into five difficulty levels, offering a broad spectrum of topics within each discipline. With VisScience, we present a detailed evaluation of the performance of 25 representative MLLMs in scientific reasoning. Experimental results demonstrate that closed-source MLLMs generally outperform open-source models. The best performance observed include a 53.4\% accuracy in mathematics by Claude3.5-Sonnet, 38.2\% in physics by GPT-4o, and 47.0\% in chemistry by Gemini-1.5-Pro. These results underscore the strengths and limitations of MLLMs, suggesting areas for future improvement and highlighting the importance of developing models that can effectively handle the diverse demands of multi-modal scientific reasoning.

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system of coupled stiff ordinary differential equations (ODEs). While deep learning techniques have been experimented with to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because deep learning methods optimize for training error without ensuring compatibility with ODE solvers, leading to accumulation of errors over time. Recently, NeuralODE-based techniques have offered a promising solution by effectively modeling chemical kinetics. In this study, we extend the NeuralODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass and the elemental mass are conserved, a critical requirement for reliable downstream integration with CFD solvers. Proof-of-concept studies are performed with physics-constrained neuralODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. Our results demonstrate that this enhancement not only improves the physical consistency with respect to mass conservation criteria but also ensures better robustness. Lastly, a posteriori studies are performed wherein the trained PC-NODE model is coupled with a 3D CFD solver for computing the chemical source terms. PC-NODE is shown to be more accurate relative to the purely data-driven neuralODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

Flamelet models are widely used in computational fluid dynamics to simulate thermochemical processes in turbulent combustion. These models typically employ memory-expensive lookup tables that are predetermined and represent the combustion process to be simulated. Artificial neural networks (ANNs) offer a deep learning approach that can store this tabular data using a small number of network weights, potentially reducing the memory demands of complex simulations by orders of magnitude. However, ANNs with standard training losses often struggle with underrepresented targets in multivariate regression tasks, e.g., when learning minor species mass fractions as part of lookup tables. This paper seeks to improve the accuracy of an ANN when learning multiple species mass fractions of a hydrogen (\ce{H2}) combustion lookup table. We assess a simple, yet effective loss weight adjustment that outperforms the standard mean-squared error optimization and enables accurate learning of all species mass fractions, even of minor species where the standard optimization completely fails. Furthermore, we find that the loss weight adjustment leads to more balanced gradients in the network training, which explains its effectiveness.

Characterizing the interior structure of exoplanets is essential for understanding their diversity, formation, and evolution. As the interior of exoplanets is inaccessible to observations, an inverse problem must be solved, where numerical structure models need to conform to observable parameters such as mass and radius. This is a highly degenerate problem whose solution often relies on computationally-expensive and time-consuming inference methods such as Markov Chain Monte Carlo. We present ExoMDN, a machine-learning model for the interior characterization of exoplanets based on Mixture Density Networks (MDN). The model is trained on a large dataset of more than 5.6 million synthetic planets below 25 Earth masses consisting of an iron core, a silicate mantle, a water and high-pressure ice layer, and a H/He atmosphere. We employ log-ratio transformations to convert the interior structure data into a form that the MDN can easily handle. Given mass, radius, and equilibrium temperature, we show that ExoMDN can deliver a full posterior distribution of mass fractions and thicknesses of each planetary layer in under a second on a standard Intel i5 CPU. Observational uncertainties can be easily accounted for through repeated predictions from within the uncertainties. We use ExoMDN to characterize the interior of 22 confirmed exoplanets with mass and radius uncertainties below 10% and 5% respectively, including the well studied GJ 1214 b, GJ 486 b, and the TRAPPIST-1 planets. We discuss the inclusion of the fluid Love number $k_2$ as an additional (potential) observable, showing how it can significantly reduce the degeneracy of interior structures. Utilizing the fast predictions of ExoMDN, we show that measuring $k_2$ with an accuracy of 10% can constrain the thickness of core and mantle of an Earth analog to $\approx13\%$ of the true values.

In this work, we present a novel physics-based data-driven framework for reduced-order modeling of laser ignition in a model rocket combustor based on parameterized neural ordinary differential equations (PNODE). Deep neural networks are embedded as functions of high-dimensional parameters of laser ignition to predict various terms in a 0D flow model including the heat source function, pre-exponential factors, and activation energy. Using the governing equations of a 0D flow model, our PNODE needs only a limited number of training samples and predicts trajectories of various quantities such as temperature, pressure, and mass fractions of species while satisfying physical constraints. We validate our physics-based PNODE on solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations of laser-induced ignition in a prototype rocket combustor. We compare the performance of our physics-based PNODE with that of kernel ridge regression and fully connected neural networks. Our results show that our physics-based PNODE provides solutions with lower mean absolute errors of average temperature over time, thus improving the prediction of successful laser ignition with high-dimensional parameters.

We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation. Specifically, we apply the deep operator network (DeepONet) along with its extensions, such as the autoencoder-based DeepONet and the newly proposed Partition-of-Unity (PoU-) DeepONet to study a range of examples, including the ROBERS problem with three species, the POLLU problem with 25 species, pure kinetics of the syngas skeletal model for $CO/H_2$ burning, which contains 11 species and 21 reactions and finally, a temporally developing planar $CO/H_2$ jet flame (turbulent flame) using the same syngas mechanism. We have demonstrated the advantages of the proposed approach through these numerical examples. Specifically, to train the DeepONet for the syngas model, we solve the skeletal kinetic model for different initial conditions. In the first case, we parametrize the initial conditions based on equivalence ratios and initial temperature values. In the second case, we perform a direct numerical simulation of a two-dimensional temporally developing $CO/H_2$ jet flame. Then, we initialize the kinetic model by the thermochemical states visited by a subset of grid points at different time snapshots. Stiff problems are computationally expensive to solve with traditional stiff solvers. Thus, this work aims to develop a neural operator-based surrogate model to solve stiff chemical kinetics. The operator, once trained offline, can accurately integrate the thermochemical state for arbitrarily large time advancements, leading to significant computational gains compared to stiff integration schemes.

Atmospheric mass-loss is known to play a leading role in sculpting the demographics of small, close-in exoplanets. Knowledge of how such planets evolve allows one to ``rewind the clock'' to infer the conditions in which they formed. Here, we explore the relationship between a planet's core mass and their atmospheric mass after protoplanetary disc dispersal by exploiting XUV photoevaporation as an evolutionary process. Historically, this style of inference problem would be computationally infeasible due to the large number of planet models required; however, we make use of a novel atmospheric evolution emulator which utilises neural networks to provide three orders of magnitude in speedup. First, we provide proof-of-concept for this emulator on a real problem, by inferring the initial atmospheric conditions to the TOI-270 multi-planet system. Using the emulator we find near-indistinguishable results when compared to original model. We then apply the emulator to the more complex inference problem, which aims to find the initial conditions for a sample of \textit{Kepler}, \textit{K2} and \textit{TESS} planets with well-constrained masses and radii. We demonstrate there is a relationship between core masses and the atmospheric mass that they retain after disc dispersal, and this trend is consistent with the `boil-off' scenario, in which close-in planets undergo dramatic atmospheric escape during disc dispersal. Thus, it appears the exoplanet population is consistent with the idea that close-in exoplanets initially acquired large massive atmospheres, the majority of which is lost during disc dispersal; before the final population is sculpted by atmospheric loss over 100~Myr to Gyr timescales.

The accurate prediction of small scales in underresolved flows is still one of the main challenges in predictive simulations of complex configurations. Over the last few years, data-driven modeling has become popular in many fields as large, often extensively labeled datasets are now available and training of large neural networks has become possible on graphics processing units (GPUs) that speed up the learning process tremendously. In fact, the successful application of deep neural networks in fluid dynamics, such as for underresolved reactive flows, is still challenging. This work advances the recently introduced PIESRGAN to reactive finite-rate-chemistry flows. However, since combustion chemistry typically acts on the smallest scales, the original approach needs to be extended. Therefore, the modeling approach of PIESRGAN is modified to accurately account for the challenges in the context of laminar finite-rate-chemistry flows. The modified PIESRGAN-based model gives good agreement in a priori and a posteriori tests in a laminar lean premixed combustion setup. Furthermore, a reduced PIESRGAN-based model is presented that solves only the major species on a reconstructed field and employs PIERSGAN lookup for the remaining species, utilizing staggering in time. The advantages of the discriminator-supported training are shown, and the usability of the new model demonstrated in the context of a model gas turbine combustor.