The cloud‐assisted intelligent systems have attracted extensive attention due to their powerful data analysis and computation capabilities. However, how to handle encrypted data remains a challenging problem in intelligent systems. A promising solution is searchable symmetric encryption (SSE), which enables a client to privately outsource their data to the cloud while preserving keyword search functionality. In practice, dynamic SSE is more practical and supports efficient data addition and deletion. Unfortunately, data update will leak some additional information which can be exploited to break data privacy. To address this issue, forward and backward secure SSE schemes are proposed to reduce the leakage of data update. That is, forward security guarantees that the newly updated documents cannot reveal the previously searched keywords, while backward security guarantees that the server cannot recover the deleted documents. However, the existing forward and backward secure SSE schemes mainly consider curious‐but‐honest server. How to verify the soundness and completeness of search results is still a challenge. In this paper, we propose a noninteractive verifiable dynamic SSE scheme with forward and backward security from two universal accumulators. Specifically, the server in our scheme only needs one roundtrip to return the nondeleted search results to the client, which saves the communication overhead dramatically. Besides, our scheme can achieve public verification that anyone can verify the search results but not only the client who has the private key. Finally, we give a formal security analysis and compare the proposed scheme with other related work, the results show that our scheme can achieve the desired security properties with practical efficiency.