The field of parametric problems is witnessing a significant shift towards adaptive methods, which enable efficient and accurate solutions for complex problems. Researchers are developing innovative techniques that combine sparse and low-rank approximations, adaptive rank approaches, and dynamical low-rank optimization to tackle challenging problems in various domains, such as elliptic PDEs, vibrational systems, and kinetic equations. These advances have the potential to significantly reduce computational costs and improve the accuracy of solutions. Noteworthy papers include:

• A paper introducing a new approximation format for parametric elliptic PDEs, which combines low-rank tensor approximation with sparse polynomial expansion.
• A study proposing an adaptive scheme for optimizing damper positions in vibrational systems, which reduces the computational cost of the optimization process.
• A work developing a mass-conserving, adaptive-rank solver for the Wigner-Poisson system, which achieves O(N) complexity in both storage and computation time.
• A paper presenting a dynamical low-rank optimizer for solving kinetic parameter identification inverse problems, which significantly reduces memory and computational costs.