Various methods and systems are provided for an exhaust gas recirculation cooler including a plurality of cooling tubes. In one example, an exhaust gas recirculation (EGR) cooler includes a plurality of cooling tubes positioned within a housing of the EGR cooler, each cooling tube of the plurality of cooling tubes extending between and directly coupled to tube sheets of the EGR cooler at ends of each cooling tube, where at least one end of one or more cooling tubes of a first portion of the plurality of cooling tubes, inward of a tube sheet coupled to the at least one end, includes a compliant region, where the first portion is positioned proximate to an exhaust inlet of the EGR cooler.