Inverse problems remain at the heart of scientific discovery and technological innovation, spanning fields as diverse as medical and satellite imaging, biology, astronomy, geophysics, environmental sciences, computer vision, energy, finance, and defence. Fundamentally, these problems involve using a mathematical or physical model “backwards” to infer a quantity of interest from the observed effects it produces. A main challenge resulting from using models “backwards” is that solutions are often not well posed, i.e., not unique or unstable with respect to small perturbations in the data. This difficulty continues to stimulate research and innovation at the interface of applied mathematics, statistics, engineering, and physics, leading to social and economic benefit through impact on science, medicine, and engineering. The aim of this conference is to bring together mathematicians, statisticians, and computer scientists working on the theoretical and numerical aspects of inverse problems, alongside engineers and physicists, tackling challenging applications. We will discuss recent developments and open challenges in theory, methodology, and computational algorithms. Joint Event: Big Data Day This year, the conference features a dedicated Big Data Day, held in conjunction with the IMA Conference on the Mathematical Challenges of Big Data. This joint session reflects the growing intersection between classical model-based theory and modern data-driven approaches. With the rise of deep learning, generative models, and neural operators, the boundary between Inverse Problems and Data Science has become increasingly blurred. This day will explore the synergy between these fields, examining how techniques from network science, information theory, and large-scale optimisation can be leveraged to address ill-posedness, and conversely, how inverse problem theory can inform the foundations of data science. We welcome industrial representatives, doctoral students, early career researchers, and established academics to attend and contribute.