Training adverbs are provided in this article. The words listed here are commonly found along with the verb training in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb TRAINING.
carefully, constantly
currently, merely
properly, simply
Hope this word list had the training adverb you were looking for. In addition to adverbs used with training, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.