The arcane expert is a wizard who has studied the fundamentals of magic, and has understood the relationship between a spell's element and magic itself.  The Arcane Expert is able to break down elemental damage into the base spell's innate force.  Increasing the effectiveness, but limiting the versatility.

Force casting

At 2nd level the wizard gains the ability to change a spell's elemental damage (Acid, cold, fire, lightning, necrotic, poison, psychic, radiant, or thunder) damage into force damage upon casting.

Force mastery

At 2nd level whenever the wizard casts a spell that deals force damage, the spell will deal an extra 1d4 force damage for the level of the spell slot used.  This applies to all attack rolls made for the spell if the spell can make multiple.

Extra potent cantrips

At 6th level the wizard can choose to expend a first level spell slot when casting a cantrip to deal double damage, or double the amount of targets the cantrip can affect.  The wizard can use this up to a number equal to their intelligence modifier.  The wizard gains all uses of this ability on a long rest.  This effect can not occur on cantrips that have innate force damage.

Arcane memory

At 10th level the wizard gains expertise in arcana, and gains advantage on arcana checks when recalling arcane based information.  The wizard also gains the ability to, when a spell is cast by an enemy or ally, use their reaction to memorize the spell.  This memorized spell can be transcribed into the wizard's spellbook for half the time and half the cost.  If the spell memorized forces a saving throw on a wizard who has memorized the spell, that wizard gains advantage on the first saving throw of the spell.

Spell mastery

At 14th level the wizard can choose 1 damaging spell with a casting time of 1 action to gain mastery over.  Mastery of a spell grants the following benefits.

- Changes the spell's damage to force if not already.

- The wizard adds their intelligence modifier to all damage rolls of the mastered spell.

- The wizard can use their bonus action while casting this spell to expend an extra spell slot of equal level to the mastered spell to double the effects of the spell.

The mastered spell can only be of 5th level or below.  To change the mastered spell the wizard must spend gold equal to the spells level x 20 on a long rest.  At 16th and 18th level the wizard can gain mastery over an additional spell to a maximum of 3 mastered spells.