Cable　force　identification　is　crucial　for　ensuring　the　safety　and　operational　performance　of　in-service　long-span　bridge　structures.　Besides　the　commonly-used　frequency　measurements　for　calculating　cable　forces　using　frequency-cable　force　relationship　formulas,　more　efficient　and　straightforward　identification　could　be　achieved　by　directly　utilizing　frequency　response　functions　(FRFs).　This　study　presents　a　novel　approach　that　employs　neural　networks　to　model　the　relationship　between　the　FRFs　and　cable　forces,　resulting　in　a　more　streamlined　method　for　identifying　cable　forces　on　long-span　bridges.　Firstly,　the　working　mechanism　of　an　auto-encoder　is　merged　with　the　unique　characteristics　of　the　FRFs,　giving　the　cross　signature　assurance　criterion.　This　criterion　is　then　integrated　into　the　loss　function　as　a　constraint　to　account　for　the　poor　interpretability　of　pure　data-driven　methodology　in　solving　engineering　problems,　leading　to　a　grey-box　data-driven　paradigm.　Following　this　paradigm,　a　physics-informed　auto-encoder　(PIAE)　network　is　employed　to　reduce　the　dimensionality　of　the　FRF　data　during　extracting　key　features.　The　reduced　FRF　data　are　paired　with　the　cable　forces　to　form　training　samples.　The　PIAE　network　is　then　trained　directly　on　these　samples　for　the　purpose　of　cable　force　identification.　Finally,　the　validation　of　the　proposed　method　was　conducted　on　the　actual　monitoring　data　from　a　cable-stayed　bridge　and　a　concrete-filled　steel　tubular　arch　bridge.　Results　indicate　that　the　proposed　method　achieves　not　only　high　prediction　accuracy,　but　also　a　good　fit　between　the　predicted　and　actual　developmental　trends　of　cable　forces,　and　is　well-suited　for　the　different　types　of　bridges.