Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from empirical data. Despite generating significant interest especially in the machine-learning community, a thorough study of realistic inverse problems in the presence of modelling error and utilization of physical measurement data is still outstanding. In this work, the framework of unconditional representation for the conditional score function (UCoS) is evaluated for linearized difference imaging in diffuse optical tomography (DOT). DOT uses boundary measurements of near-infrared light to estimate the spatial distribution of absorption and scattering parameters in biological tissues. The problem is highly ill-posed and thus sensitive to noise and modelling errors. We introduce a novel regularization approach that prevents overfitting of the score function by constructing a mixed score composed of a learned and a model-based component. Validation of this approach is done using both simulated and experimental measurement data. The experiments demonstrate that a data-driven prior distribution results in posterior samples with low variance, compared to classical model-based estimation, and centred around the ground truth, even in the context of a highly ill-posed problem and in the presence of modelling errors.

The search for biologically faithful synaptic plasticity rules has resulted in a large body of models. They are usually inspired by -- and fitted to -- experimental data, but they rarely produce neural dynamics that serve complex functions. These failures suggest that current plasticity models are still under-constrained by existing data. Here, we present an alternative approach that uses meta-learning to discover plausible synaptic plasticity rules. Instead of experimental data, the rules are constrained by the functions they implement and the structure they are meant to produce.

Advances in artificial intelligence (AI) have made AI-driven scientific discovery a highly promising new paradigm [1]. Although AI has achieved remarkable results in tackling domain-specific challenges [2, 3], the ultimate aspiration from a paradigm-shifting perspective still lies in developing reliable AI systems capable of autonomous scientific discovery directly from a large collection of raw data without supervision [4, 5]. Current approaches to automated physics discovery focus on individual experiments, employing either neural network (NN)-based methods [6-25] or symbolic techniques [26-33]. By analyzing data from a single experiment, these methods can construct a specific model capable of predicting future data from the same experiment; if sufficiently simple, such a model may even be expressed in symbolic form [34-36]. Although these methods represent a crucial and successful stage towards automated scientific discovery, they have not yet reached a discovery capacity comparable to that of human physicists.

Understanding and predicting polymer solubility in various solvents is critical for applications ranging from recycling to pharmaceutical formulation. This work presents a deep learning framework that predicts polymer solubility, expressed as weight percent (wt%), directly from SMILES representations of both polymers and solvents. A dataset of 8,049 polymer solvent pairs at 25 deg C was constructed from calibrated molecular dynamics simulations (Zhou et al., 2023), and molecular descriptors and fingerprints were combined into a 2,394 feature representation per sample. A fully connected neural network with six hidden layers was trained using the Adam optimizer and evaluated using mean squared error loss, achieving strong agreement between predicted and actual solubility values. Generalizability was demonstrated using experimentally measured data from the Materials Genome Project, where the model maintained high accuracy on 25 unseen polymer solvent combinations. These findings highlight the viability of SMILES based machine learning models for scalable solubility prediction and high-throughput solvent screening, supporting applications in green chemistry, polymer processing, and materials design.

This paper reports an attempt to model the system dynamics and estimate both the unknown internal control input and the state of a recently developed marine autonomous vehicle, the Jaiabot. Although the Jaiabot has shown promise in many applications, process and sensor noise necessitates state estimation and noise filtering. In this work, we present the first surge and heading linear dynamical model for Jaiabots derived from real data collected during field testing. An adaptive input estimation algorithm is implemented to accurately estimate the control input and hence the state. For validation, this approach is compared to the classical Kalman filter, highlighting its advantages in handling unknown control inputs.

Heterogeneous Treatment Effect (HTE) and Conditional Average Treatment Effect (CATE) models relax the assumption that treatment effects are the same for every user. We present a large scale industrial framework for estimating HTE using experimental data from hundreds of millions of Snapchat users. By combining results across many experiments, the framework uncovers latent user characteristics that were previously unmeasurable and produces stable treatment effect estimates at scale. We describe the core components that enabled this system, including experiment selection, base learner design, and incremental training. We also highlight two applications: user influenceability to ads and user sensitivity to ads. An online A/B test using influenceability scores for targeting showed an improvement on key business metrics that is more than six times larger than what is typically considered significant.

Foundational Machine Learning Potentials can resolve the accuracy and transferability limitations of classical force fields. They enable microscopic insights into material behavior through Molecular Dynamics simulations, which can crucially expedite material design and discovery. However, insufficiently broad and systematically biased reference data affect the predictive quality of the learned models. Often, these models exhibit significant deviations from experimentally observed phase transition temperatures, in the order of several hundred kelvins. Thus, fine-tuning is necessary to achieve adequate accuracy in many practical problems. This work proposes a fine-tuning strategy via top-down learning, directly correcting the wrongly predicted transition temperatures to match the experimental reference data. Our approach leverages the Differentiable Trajectory Reweighting algorithm to minimize the free energy differences between phases at the experimental target pressures and temperatures. We demonstrate that our approach can accurately correct the phase diagram of pure Titanium in a pressure range of up to 5 GPa, matching the experimental reference within tenths of kelvins and improving the liquid-state diffusion constant. Our approach is model-agnostic, applicable to multi-component systems with solid-solid and solid-liquid transitions, and compliant with top-down training on other experimental properties. Therefore, our approach can serve as an essential step towards highly accurate application-specific and foundational machine learning potentials.

Forecasting tumor growth is critical for optimizing treatment. Classical growth models such as the Gompertz and Bertalanffy equations capture general tumor dynamics but may fail to adapt to patient-specific variability, particularly with limited data available. In this study, we leverage Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs), two pillars of Scientific Machine Learning (SciML), to construct adaptive tumor growth models capable of learning from experimental data. Using the Gompertz model as a baseline, we replace rigid terms with adaptive neural networks to capture hidden dynamics through robust modeling in the Julia programming language. We use our models to perform forecasting under data constraints and symbolic recovery to transform the learned dynamics into explicit mathematical expressions. Our approach has the potential to improve predictive accuracy, guiding dynamic and effective treatment strategies for improved clinical outcomes.