Understanding the computational capacity of molecular systems is important both for basic insights into information processing in biological systems and the design of synthetic nano/micro-scale technologies. Here, we design systems that, instead of mimicking conventional engineered computational systems, exploit intrinsic physical dynamics to carry out pattern recognition autonomously. Using chemical reaction networks and self-assembly of many heterogeneous species, we demonstrate pattern recognition capabilities on pulsatile temporal inputs and high-dimensional concentration patterns. Throughout, we emphasize the ways in which our physical mechanisms are naturally suited to the particular computational challenges. This work not only provides molecular computational solutions for concrete problems, but also helps broaden the paradigm about how, when, and where computation can occur in molecular systems.