Not able to save the values in rule input

Look on Appian example: https://docs.appian.com/suite/help/21.1/Editable_Grid_Component.html

hard to review entier code but your local!publication is Array of type type!{urn:com:appian:types:ISR}ISR_StudyDetail so you in below code you are trying to add to that array Today() +1 (save!value). 

If you want to append local!publication you need to add another object of type type!{urn:com:appian:types:ISR}ISR_StudyDetail

addRowlink: a!dynamicLink(
label: "Add Publication Details",
value: {
startDate: today() + 1
},
saveInto: {
a!save(local!publication, append(local!publication, save!value))
}
),

a!localVariables(
  local!publication: cast(
    typeof(
      'type!{urn:com:appian:types}studyDetail'()
    ),
    {}
  ),
  a!boxLayout(
    label: "Publicaton Plan",
    contents: {
      a!gridLayout(
        totalCount: count(local!publication),
        headerCells: {
          a!gridLayoutHeaderCell(label: "Publication Type"),
          a!gridLayoutHeaderCell(label: "Publication Name"),
          a!gridLayoutHeaderCell(label: "Year Estimate"),
          /* For the "Remove" column */
          a!gridLayoutHeaderCell(label: "")
        },
        columnConfigs: {
          a!gridLayoutColumnConfig(width: "DISTRIBUTE", weight: 3),
          a!gridLayoutColumnConfig(width: "DISTRIBUTE", weight: 3),
          a!gridLayoutColumnConfig(width: "DISTRIBUTE", weight: 3),
          a!gridLayoutColumnConfig(width: "ICON")
        },
        rows: a!forEach(
          items: local!publication,
          expression: a!gridRowLayout(
            contents: {
              a!radioButtonField(
                label: "Publication Type",
                value: fv!item.publicationType,
                saveInto: fv!item.publicationType,
                required: true(),
                choiceLabels: { "Conference", "Journal" },
                choiceValues: { "Conference", "Journal" },
                choiceLayout: "COMPACT"
              ),
              a!paragraphField(
                label: "Publication Name",
                /*instructions: rule!ISR_er_InstructionsText(*/
                /*data: fv!item.publicationName,*/
                /*maxLength: cons!ISR_PARAGRAPH_LENGTH*/
                /*),*/
                /*not sure why u need refresh*/
                /*refreshAfter: "KEYPRESS",*/
                value: fv!item.publicationName,
                saveInto: {
                  clean(fv!item.publicationName),
                  /*not sure on the study details type for now commenting*/
                  /*a!save(fv!item.publicationName,*/
                  /*ri!studyDetail.publicationName*/
                  /*),*/
                  /**/
                  
                },
                required: true(),
                /*validationGroup: cons!ISR_VALIDATION_GROUP_SUBMIT,*/
                /*validations: rule!ISR_er_ValidateTextLength(*/
                /*text: fv!item.publicationName,*/
                /*textLengthAllowed: cons!ISR_PARAGRAPH_LENGTH*/
                /*),*/
                
              ),
              a!dropdownField(
                label: "Year estimate",
                placeholder: "--- Select a Year ---",
                choiceLabels: cons!ISR_yearlistforpublication,
                choiceValues: cons!ISR_yearlistforpublication,
                value: fv!item.estimatedYear,
                saveInto: fv!item.estimatedYear,
                required: true()
              ),
              a!richTextDisplayField(
                value: a!richTextIcon(
                  icon: "close",
                  altText: "delete " & fv!index,
                  caption: "Remove " & fv!item.publicationType & " " & fv!item.publicationName,
                  link: a!dynamicLink(
                    value: fv!index,
                    saveInto: {
                      a!save(
                        local!publication,
                        remove(local!publication, save!value)
                      )
                    }
                  ),
                  linkStyle: "STANDALONE",
                  color: "NEGATIVE"
                )
              )
            },
            id: fv!index
          )
        ),
        addRowlink: a!dynamicLink(
          label: "Add Publication Details",
          saveInto: {
            a!save(
              local!publication,
              append(local!publication, save!value)
            )
          }
        ),
        rowHeader: 1
      )
    },
    iscollapsible: true,
    isInitiallyCollapsed: false(),
    marginBelow: "STANDARD"
  )
)

I tried to debug the code and added the comments as well. Check the above code whether it is working for your requirement 

Hi Saranya,

columns "Publication Type" and "Year Estimate" inputs are getting stored in local variables but not in rule inputs.

"Publication Name" column inputs/data not getting saved neither local or rule inputs.

Hi Shafi,

I would say, you can add and update using local variables and on the submit/ update button save the local variable to rule input

Hi,

I would suggest the same if your ri and local are of same type