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Realizing a multifunctional integrated photonic platform is one of the goals for future optical information processing, which usually requires large size to realize due to multiple integration challenges. Here, we realize a multifunctional integrated photonic platform with ultracompact footprint based on inverse design. The photonic platform is compact with 86 inverse designed-fixed couplers and 91 phase shifters. The footprint of each coupler is 4 μm by 2 μm, while the whole photonic platform is 3 mm by 0.2 mm-one order of magnitude smaller than previous designs. One-dimensional Floquet Su-Schrieffer-Heeger model and Aubry-André-Harper model are performed with measured fidelities of 97.90 (±0.52) % and 99.34 (±0.44) %, respectively. We also demonstrate a handwritten digits classification task with the test accuracy of 87% using on-chip training. Moreover, the scalability of this platform has been proved by demonstrating more complex computing tasks. This work provides an effective method to realize an ultrasmall integrated photonic platform.