Is there a way to find out if my fuel regulator is bad on my 2004 Chevy aveo

A dirty air filter, clogged or worn PCV valve or clogged EGR valve can cause engine surging. If those don't take care of the problem, get an ODB scan tool and watch what the engine is doing when it surges - especially the oxygen sensor output, injector dwell times and ignition timing (bring along a knowledgeable passenger to watch the tool while you drive, or get someone else to drive). Patterns here can give you a clue. Any check engine codes should be investigated. By now, you've spent enough money throwing parts at the problem to buy one of these, but many auto parts stores will let you rent or borrow one.

One item to particularly watch on the scan tool is injector dwell time. If the timings are highly variable at idle, the fuel pressure regulator may be bad. (Another symptom of a bad regulator is intermittent hard cold starting, and an odor of raw gas in the exhaust when the engine is cold. Prolonged or frequent operation at low RPM with a bad fuel pressure regulator can ruin a catalytic converter.)

Other causes of catalytic converter failure may also be behind the surging issue. Also, the engine computer is programmed with the assumption that there is a catalytic converter, so the reduced back pressure may be destabilizing the control loop that kicks in when the engine is warmed up.

The RockAuto catalytic converter pages list common causes of converter failure that should be checked before ordering a replacement. It's worth a look. Here's the link for your vehicle: Click the info button for any of the converters offered. If your state requires you to install a CARB-compliant converter, you may want to look for a used one.

2253, 3116, 3451, 2152, 4362, 4316
4316, 4513, 4362, 1156, 2145, 1156
6451, 6361, 5624, 5241, 3346, 1165
3241, 4524, 5436, 5813, 3265, 5624
2453, 3462, 3251, 5445, 8253, 1156
2346, 4853, 6645, 5253, 1325, 4136
3116, 3221, 2151, 5312, 2654, 4314
These has worked every time for me. Please, comment and such if these have helped.

i cleaned the egr valve on mine solved the problem

Could be a fuel pump failure

You don't always get a code for every
vehicle problem

Takes some old school thinking & testing
to find these issues

I had a corolla that did this to me, turned out to be an injector. Definitely worth looking towards that.

1 Inspect Choke Thermostat Stuck or Improperly Functioning Choke Thermostat. 2 Inspect Fuel Filter Clogged or Dirty Fuel Filter. 3 Inspect Relay - Fuel Pumpat Faulty Fuel Pump Relay. 4 Inspect Fuel Injector Pressure Regulator Faulty Fuel Injector Pressure Regulator. 5 Inspect Fuel Pump Low Fuel Pressure. 6 Inspect Engine Control Computer Incorrect Operating Information Being Delivered and Sent From The EEC. 7 Inspect Fuel Pump Strainer Clogged or Dirty Fuel Pump Strainerat.

could be a fuel pump or a timing belt.

There is a Communication problem between the Transmission Control Module (TCM) and the Engine control module. That is the bad news and is why it's shutting down the engine. 
The good news is i believe there is a TSB recall on the 2004 - 2007 chevy aveo for the P0700 problem so it should be covered under warranty. 
Believe the TSB# 05-06-01-030D
Good luck and hope this helps and hope it's not a bad ECM. Check the wire harness to the ECM and TCM, look for broken wire or the harness it self gone apart. 

try giving your car a simple service, change oil, oil filter, air filter, plugs and leads etc. also get your wheels aligned and balanced as having bad geo can also be bad for fuel consumption. if that doesnt work then id recomend a garage.