The recent developments in computational and applied mathematics highlight a significant shift towards enhancing the efficiency and accuracy of numerical methods through innovative approaches. A notable trend is the integration of machine learning techniques with traditional numerical methods to address complex inverse problems and improve computational efficiency. For instance, neural networks are being employed to accelerate Markov Chain Monte Carlo (MCMC) methods, offering substantial speedups without compromising accuracy. Similarly, the application of conditional diffusion models to ill-posed problems, such as electrical impedance tomography, demonstrates the potential of deep learning in improving image reconstruction quality. Another emerging direction is the use of normalizing flows within MCMC frameworks, which has shown promise in preconditioning target distributions and enabling more efficient sampling. Furthermore, the development of comprehensive datasets and benchmarks, particularly in the context of wearable technology and cardiovascular simulations, is facilitating more robust and reliable predictions in real-world scenarios. These advancements underscore a broader movement towards leveraging data-driven methods and computational innovations to tackle challenging problems in applied mathematics and beyond.

Noteworthy Papers

• Transport Quasi-Monte Carlo: Introduces a novel method for improving the accuracy of Quasi-Monte Carlo in high-dimensional integrals through a transport map, achieving faster convergence rates.
• MCMC-Net: Proposes a neural network-based approach to significantly accelerate MCMC methods, demonstrating up to twelvefold speedups in inverse problems.
• A Conditional Diffusion Model for Electrical Impedance Tomography Image Reconstruction: Presents a new method for EIT reconstruction using conditional diffusion models, outperforming state-of-the-art techniques.
• Empirical evaluation of normalizing flows in Markov Chain Monte Carlo: Provides the first comprehensive guidelines for selecting normalizing flow architectures in MCMC, enhancing sampling efficiency.
• WildPPG: A Real-World PPG Dataset of Long Continuous Recordings: Introduces a novel dataset for PPG recordings in outdoor environments, improving the robustness of heart rate estimation methods.
• Leveraging Cardiovascular Simulations for In-Vivo Prediction of Cardiac Biomarkers: Develops a framework for predicting cardiac biomarkers from arterial pressure waveforms, validated in both in silico and in vivo settings.
• Optimal quadrature for weighted function spaces on multivariate domains: Establishes optimal quadrature errors for weighted Sobolev and Besov classes, demonstrating the advantages of randomized algorithms.