We study Bayesian automated mechanism design in unstructured dynamic environments, where a principal repeatedly interacts with an agent, and takes actions based on the strategic agent's report of the current state of the world. Both the principal and the agent can have arbitrary and potentially different valuations for the actions taken, possibly also depending on the actual state of the world. Moreover, at any time, the state of the world may evolve arbitrarily depending on the action taken by the principal. The goal is to compute an optimal mechanism which maximizes the principal's utility in the face of the self-interested strategic agent. We give an efficient algorithm for computing optimal mechanisms, with or without payments, under different individual-rationality constraints, when the time horizon is constant.

We study Bayesian automated mechanism design in unstructured dynamic environments, where a principal repeatedly interacts with an agent, and takes actions based on the strategic agent's report of the current state of the world. Both the principal and the agent can have arbitrary and potentially different valuations for the actions taken, possibly also depending on the actual state of the world. Moreover, at any time, the state of the world may evolve arbitrarily depending on the action taken by the principal. The goal is to compute an optimal mechanism which maximizes the principal's utility in the face of the self-interested strategic agent. We give an efficient algorithm for computing optimal mechanisms, with or without payments, under different individual-rationality constraints, when the time horizon is constant.

We develop a versatile new methodology for multidimensional mechanism design that incorporates side information about agent types to generate high social welfare and high revenue simultaneously. Prominent sources of side information in practice include predictions from a machine-learning model trained on historical agent data, advice from domain experts, and even the mechanism designer's own gut instinct. In this paper we adopt a prior-free perspective that makes no assumptions on the correctness, accuracy, or source of the side information.

We develop a versatile new methodology for multidimensional mechanism design that incorporates side information about agent types to generate high social welfare and high revenue simultaneously. Prominent sources of side information in practice include predictions from a machine-learning model trained on historical agent data, advice from domain experts, and even the mechanism designer's own gut instinct. In this paper we adopt a prior-free perspective that makes no assumptions on the correctness, accuracy, or source of the side information.

The electrochemical reduction of atmospheric CO$_2$ into high-energy molecules with renewable energy is a promising avenue for energy storage that can take advantage of existing infrastructure especially in areas where sustainable alternatives to fossil fuels do not exist. Automated laboratories are currently being developed and used to optimize the composition and operating conditions of gas diffusion electrodes (GDEs), the device in which this reaction takes place. Improving the efficiency of GDEs is crucial for this technology to become viable. Here we present a modeling framework to efficiently explore the high-dimensional parameter space of GDE designs in an active learning context. At the core of the framework is an uncertainty-aware physics model calibrated with experimental data. The model has the flexibility to capture various input parameter spaces and any carbon products which can be modeled with Tafel kinetics. It is interpretable, and a Gaussian process layer can capture deviations of real data from the function space of the physical model itself. We deploy the model in a simulated active learning setup with real electrochemical data gathered by the AdaCarbon automated laboratory and show that it can be used to efficiently traverse the multi-dimensional parameter space.

Additional Feedback: 0. The notations in the method section especially Section 2 need to be specified, even if it is easy to infer from context,. For example, L_v, v_i, v_j etc. need to be explained. Further, in the case studies sections, the descriptions are not clear, for example, the system should be explained mathematically from a n-body perspective, clearly denoting the particles as nodes at gnn equation level for atleast one case. The authors should discuss the intuitions behind their specific model decisions, for example, as this is a model discovery task, why haven't the authors used generative model frameworks? 2. The input/output dimensionality for eureqa fitting should be explained in Section 3, for example, GNs have multiple layers, how does the proposed method fit equations for the edge/node functions at different layers and put them together? From the simulation dataset, the underlying model does not seem to need multiple layers for GNs. 3. The Hamiltonian Dynamics section is very hard to read, especially to a non-physics person, it would be helpful if the authors add a clear description of the input (like position and momentum) and output for the HGN. 4. What is the intuition behind the sum of pairwise and self for the HGN? Have the authors compared to a model without this assumption? 5. Does the Bottleneck model perform worse simply because its a much smaller model than the other models with a large hidden size? 6. Line 170 states that "models are trained to predict acceleration given current state", do the authors not account for time dependence?

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.

Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding of the problem at hand, subsequent mathematical formulation, and numerical approximation. Data-driven models instead aim to extract relations between input and output data without arguing any causality principle underlining the available data distribution. In recent years, data-driven models have been rapidly developed and popularized. Such a diffusion has been triggered by a huge availability of data (the so-called big data), an increasingly cheap computing power, and the development of powerful machine learning algorithms. SciML leverages the physical awareness of physics-based models and, at the same time, the efficiency of data-driven algorithms. With SciML, we can inject physics and mathematical knowledge into machine learning algorithms. Yet, we can rely on data-driven algorithms' capability to discover complex and non-linear patterns from data and improve the descriptive capacity of physics-based models. After recalling the mathematical foundations of digital modelling and machine learning algorithms, and presenting the most popular machine learning architectures, we discuss the great potential of a broad variety of SciML strategies in solving complex problems governed by partial differential equations. Finally, we illustrate the successful application of SciML to the simulation of the human cardiac function, a field of significant socio-economic importance that poses numerous challenges on both the mathematical and computational fronts. The corresponding mathematical model is a complex system of non-linear ordinary and partial differential equations describing the electromechanics, valve dynamics, blood circulation, perfusion in the coronary tree, and torso potential. Despite the robustness and accuracy of physics-based models, certain aspects, such as unveiling constitutive laws for cardiac cells and myocardial material properties, as well as devising efficient reduced order models to dominate the extraordinary computational complexity, have been successfully tackled by leveraging data-driven models.

Healthcare decision-making requires not only accurate predictions but also insights into how factors influence patient outcomes. While traditional Machine Learning (ML) models excel at predicting outcomes, such as identifying high risk patients, they are limited in addressing what-if questions about interventions. This study introduces the Probabilistic Causal Fusion (PCF) framework, which integrates Causal Bayesian Networks (CBNs) and Probability Trees (PTrees) to extend beyond predictions. PCF leverages causal relationships from CBNs to structure PTrees, enabling both the quantification of factor impacts and simulation of hypothetical interventions. PCF was validated on three real-world healthcare datasets i.e. MIMIC-IV, Framingham Heart Study, and Diabetes, chosen for their clinically diverse variables. It demonstrated predictive performance comparable to traditional ML models while providing additional causal reasoning capabilities. To enhance interpretability, PCF incorporates sensitivity analysis and SHapley Additive exPlanations (SHAP). Sensitivity analysis quantifies the influence of causal parameters on outcomes such as Length of Stay (LOS), Coronary Heart Disease (CHD), and Diabetes, while SHAP highlights the importance of individual features in predictive modeling. By combining causal reasoning with predictive modeling, PCF bridges the gap between clinical intuition and data-driven insights. Its ability to uncover relationships between modifiable factors and simulate hypothetical scenarios provides clinicians with a clearer understanding of causal pathways. This approach supports more informed, evidence-based decision-making, offering a robust framework for addressing complex questions in diverse healthcare settings.

Recent advancements in machine learning-based methods have demonstrated great potential for improved property prediction in material science. However, reliable estimation of the confidence intervals for the predicted values remains a challenge, due to the inherent complexities in material modeling. This study introduces a novel approach for uncertainty quantification in fatigue life prediction of metal materials based on integrating knowledge from physics-based fatigue life models and machine learning models. The proposed approach employs physics-based input features estimated using the Basquin fatigue model to augment the experimentally collected data of fatigue life. Furthermore, a physics-informed loss function that enforces boundary constraints for the estimated fatigue life of considered materials is introduced for the neural network models. Experimental validation on datasets comprising collected data from fatigue life tests for Titanium alloys and Carbon steel alloys demonstrates the effectiveness of the proposed approach. The synergy between physics-based models and data-driven models enhances the consistency in predicted values and improves uncertainty interval estimates.